Thierry Penduff
email: thierry.penduff@cnrs.fr

Willia Llovel

Sally Close

Ixetl Garcia-Gomez

Stéphanie Leroux

Trends of Coastal Sea Level Between 1993 and 2015: Imprints of Atmospheric Forcing and Oceanic Chaos

Keywords: Sea-level trend, Coastal ocean, Ensemble modeling, Intrinsic variability, Detection and attribution

The observation and simulation of the variability of coastal sea level are impacted by various uncertainties, such as measurement errors and sampling biases, unresolved processes, and model and forcing biases. Ocean model simulations suggest that another uncertainty should be taken into account for the attribution of sea-level changes. Global ocean simulations indeed show that resolving mesoscale turbulence (even partly) promotes the emergence of low-frequency (LF) chaotic intrinsic variability (CIV) which causes substantial random fluctuations of sea level up to multiple decades in eddy-active regions of the world ocean. This random LFCIV is superimposed on the atmospherically forced (or simply "forced") fluctuations, which are directly controlled by the atmospheric variability. We show from a large ensemble of global oceanic hindcasts that this multi-decadal LFCIV leaves a substantial imprint on the long-term trends of coastal sea level: over 17-20% of the global ocean coastal area, in particular along the coastlines of the northwestern Pacific and Indian Oceans, and around the Gulf of Mexico, random sealevel trends may blur their atmospherically forced counterpart, such that simulated (and potentially observed) coastal sea-level trends cannot be unambiguously attributed to atmospheric or anthropic causes. The steric and manometric sea-level change contributions of these uncertainties are discussed, suggesting that they mostly come from the manometric sea-level trends near the coasts.

Introduction and Context

Open Ocean and Coastal Sea-Level Evolution

The remote observation of sea level has reached an unprecedented level of accuracy and spatio-temporal coverage with the launch of the Topex/Poseidon altimeter satellite in 1992, followed by several successors up to the present day. Data from these successive missions have been inter-calibrated and merged into gridded fields, providing a continuous quasiglobal monitoring of sea level at a spatio-temporal resolution ranging from the scale of mesoscale eddies to the global ocean, and from weekly timescales to more than two decades [START_REF] Ablain | Satellite altimetry-based sea level at global and regional scales[END_REF]WCRP Global Sea Level Budget Group 2018). These data have yielded tremendous progress in physical oceanography for the description, understanding, modeling, and forecasting of the evolution of sea level (as well as related variables, including below the surface) over a wide range of scales.

Anthropogenic global warming is mostly being transferred to the ocean [START_REF] Church | Revisiting the Earth's sea-level and energy budgets from 1961 to 2008[END_REF][START_REF] Rhein | Observations: ocean. Chapter 3 in climate change 2013: the physical science basis[END_REF]) and has a particularly clear imprint on global mean sea level, with a linear rise of 3 ± 0.4 mm year -1 since 1993 [START_REF] Nerem | Climatechange-driven accelerated sea-level rise detected in the altimeter era[END_REF]. This globally averaged increase is mostly due to the thermal expansion of sea water (known as thermosteric sealevel contribution), and to the melting of ice sheets from Greenland and Antarctica and mountain glaciers. The continental freshwater input has a global imprint on global mean sea-level rise and is known as barystatic sea-level rise [START_REF] Gregory | Concepts and terminology for sea level: mean, variability and change, both local and global[END_REF]). At regional scale, other physical processes are at play such as salinity changes that can compensate or enhance temperature changes [START_REF] Llovel | Importance and origin of halosteric contribution to sea level change in the southeast Indian Ocean during 2005-2013[END_REF], ocean dynamics and circulation (affecting seawater properties), atmospheric heat fluxes, precipitation, and evaporation [START_REF] Church | Sea level change[END_REF]. The observed trends of sea level in fact have a complex and slowly varying spatial structure controlled by many oceanic and atmospheric processes, the geometry of ocean basins and coasts, the vertical displacements of the latter, etc. This means that in certain coastal regions, the observed sea-level trend can be substantially smaller or larger than its global average, raising in the latter case serious environmental concerns within highly populated coastal areas around the globe.

The monitoring, understanding, and mitigation of sea-level changes require accurate and stable measurements of open ocean and coastal sea level over long periods (see [START_REF] Marcos | Coastal sea level and related fields from existing observing systems[END_REF], together with numerical and process-oriented studies of the ocean dynamics. Another important issue also requires attention: it concerns the estimation of uncertainties associated with the measurements and processes of long-term sea-level variations, which are particularly large in coastal regions.

Low-Frequency Chaotic Intrinsic Variability (LFCIV) in the Ocean

One specific uncertainty about the low-frequency oceanic variations of regional sea level has been somewhat overlooked until recently and is now being recognized as substantial in the open ocean. Global ocean/sea-ice simulations, and especially those performed in the eddying regime (with grid spacings of 1/4° and finer) show that nonlinear ocean dynamics spontaneously produce a Low-Frequency Chaotic Intrinsic Variability (LFCIV), even without any low-frequency atmospheric forcing. [START_REF] Penduff | Sea-level expression of intrinsic and forced ocean variabilities at interannual time scales[END_REF] and [START_REF] Sérazin | Intrinsic variability of sealevel from global 1/12° ocean simulations: spatio-temporal scales[END_REF] have shown from long global ocean/sea-ice high-resolution simulations, repeatedly forced by the same annual cycle, that the LFCIV leaves a large imprint on sea level in many regions of the open ocean, and may explain in certain midlatitudes eddy-active regions up to 100% of the full interannual-to-decadal sea-level variability simulated in a hindcast. 1This LFCIV questions the attribution to atmospheric or anthropic drivers of regional sealevel variability or long-term changes: the LFCIV in the turbulent ocean consists of a persistent low-frequency spatially-structured "noise" (with a random phase and an intermittent character) that may blur or even dominate the "signal" (i.e., the atmospherically forced variations) that is directly driven by the evolution of the external forcing. It is important to note that LFCIV is much weaker in non-turbulent ocean models2 [START_REF] Penduff | Sea-level expression of intrinsic and forced ocean variabilities at interannual time scales[END_REF], suggesting that the coarse-resolution ocean components of coupled climate models used for climate projections largely underestimate this source of uncertainty. [START_REF] Sérazin | Inverse cascades of kinetic energy as a source of intrinsic variability: a global OGCM study[END_REF] demonstrated that nonlinear interactions between mesoscale (turbulent, chaotic) eddies at subannual timescales spontaneously and persistently feed sealevel variability at longer timescales (i.e., decadal in the Southern Ocean). 3 This temporal inverse cascade is at work in 1/4° and 1/12° global ocean simulations; this process is basically equally strong under seasonal atmospheric forcing and under full reanalyzed forcing, and may thus be an important source of LFCIV in oceanic hindcasts.

Disentangling the LFCIV and the Atmospherically Forced Ocean Variability

The model studies mentioned above took advantage of pairs of simulations: a climatological run that isolates the LFCIV under repeated seasonal forcing, and a hindcast (driven by an atmospheric reanalysis including interannual variability) that simulates the "full" lowfrequency ocean variability. These results suggested that the full ocean variability in this eddying regime might be a blend of LFCIV and atmospherically forced variability [START_REF] Penduff | Sea-level expression of intrinsic and forced ocean variabilities at interannual time scales[END_REF]. Pairs of simulations, however, are not sufficient to properly disentangle both components.

In order to separate both components, the OCCIPUT project produced a large ensemble (50 members) of 1/4°-resolution global ocean/sea-ice NEMO-based simulations [START_REF] Penduff | Ensembles of eddying ocean simulations for climate[END_REF], Bessières et al. 2017). As explained in the next section, the integration strategy was designed to separate, quantify, and characterize the forced variability that is directly driven by the atmospheric variability, and the chaotic intrinsic variability (abbreviated as LFCIV for low frequencies) whose phase differs in each member, and which is independent of the atmospheric evolution.

Studies based on 1/4° and 1/12° climatological simulations have shown that the LFCIV not only has a strong imprint on sea level, but also on the Atlantic Meridional Overturning simulation (AMOC; see [START_REF] Hirschi | A monitoring design for the Atlantic meridional overturning circulation[END_REF][START_REF] Grégorio | Intrinsic variability of the Atlantic meridional overturning circulation at interannual-to-multidecadal time scales[END_REF]. Analyses of the OCCIPUT ensemble have further demonstrated that the LFCIV, now diagnosed from ensemble statistics, remains comparable in amplitude to its counterpart in climatological runs [START_REF] Leroux | Intrinsic and atmospherically forced variability of the AMOC: insights from a large-ensemble ocean hindcast[END_REF], and impacts other important climate-relevant oceanic variables: the interannual-to-decadal variability of ocean heat content (OHC) was, for example, shown to be dominantly chaotic in several regions of the global ocean [START_REF] Sérazin | A global probabilistic study of the ocean heat content low-frequency variability: atmospheric forcing versus oceanic chaos[END_REF].

While the globally integrated OHC interannual-to-decadal variability is almost totally forced by the atmosphere in the OCCIPUT ensemble, the LFCIV impact on certain largescale climate-relevant oceanic indices can remain substantial at very large spatial scales. [START_REF] Zanna | Uncertainty and scale interactions in ocean ensembles: from seasonal forecasts to multi-decadal climate predictions[END_REF] thus showed that between 40 and 48°S, the LFCIV accounts for about 30% of the monthly to multi-decadal variability of the Meridional Heat Transport integrated over the whole range of longitudes.

Impacts of the Forcing and of the LFCIV on Long-Term Oceanic Trends

The chaotic component of the eddying ocean variability can exert a significant influence even at timescales of multiple decades and thus has an imprint on long-term trends. [START_REF] Sérazin | Quantifying uncertainties on regional sea-level rise induced by multi-decadal oceanic intrinsic variability[END_REF] showed from a long climatological 1/4° NEMO simulation that multi-decadal LFCIV in strongly eddying regions may manifest itself as random sea-level trends over several decades. [START_REF] Sérazin | A global probabilistic study of the ocean heat content low-frequency variability: atmospheric forcing versus oceanic chaos[END_REF] further showed that in such regions the 30-year trends of OHC fields, computed between 1980 and 2010 from the OCCIPUT ensemble, may also be mostly due to the oceanic chaos and not to the atmospheric (or anthropogenic) forcing. [START_REF] Llovel | Contributions of atmospheric forcing and chaotic ocean variability to regional sea level trends over 1993-2015[END_REF] showed that similar results hold for regional sea-level trends in many regions of the open ocean over the altimetric period .

These results strongly suggest that attributing low-frequency ocean variability, and certain long-term trends, to external (atmospheric, or anthropogenic) drivers is not straightforward in the eddying ocean. The ocean-driven multi-decadal LFCIV may manifest itself in certain finite-length time series as significant random trends. This raises important issues regarding the detection and attribution of oceanic changes in numerical simulations, and presumably in observations.

The aforementioned studies were, however, focused on the impacts of the LFCIV and atmospheric variability in the open ocean and gave no particular consideration to coastal regions. In this study, the OCCIPUT ensemble simulation is analyzed to disentangle the respective imprints of the atmospheric forcing and the low-frequency oceanic chaos on regional sea-level trends over the altimetric period , in particular in coastal regions. This paper addresses the following questions:

• How are the forced and random sea-level trends distributed in the coastal ocean?

• Where is the signal-to-noise ratio (ratio between the forced and random trends) largest and smallest in the coastal ocean? • What are the contributions of steric and manometric (i.e., non-steric or bottom pressure changes, [START_REF] Gregory | Concepts and terminology for sea level: mean, variability and change, both local and global[END_REF]) effects in the forced and random sea-level trends in the coastal ocean? • What are the implications of the above issues for the monitoring, analysis and forecast of sea-level trends?

Section 2 presents the OCCIPUT ensemble simulation, and the post-processing applied to the model outputs. Section 3 presents the respective imprints of forced and random sealevel trends, with a specific focus on coastal and shallow regions. Conclusions are given and discussed in the last section.

Post-processing of Model and Observed Data

The partners of the OCCIPUT project (OceaniC Chaos-ImPacts, strUcture, predicTability, [START_REF] Penduff | Ensembles of eddying ocean simulations for climate[END_REF] performed two kinds of 1/4° ocean/sea-ice simulations drawing on a common global model configuration based on NEMO3.5 [START_REF] Bessières | Development of a probabilistic ocean modelling system based on NEMO 3.5: application at eddying resolution[END_REF]): the ensemble run presented above consists in 50 hindcasts with perturbed initial conditions, driven over 1960-2015 by the DFS5.2 forcing fields (based on ERA-Interim, see Dussin and Barnier 2013); a companion climatological simulation was repeatedly forced during 330 years by a climatological atmospheric annual cycle derived from DFS5.2. (This forcing is devoid of any low-frequency and trend.) The integration strategy is detailed in [START_REF] Leroux | Intrinsic and atmospherically forced variability of the AMOC: insights from a large-ensemble ocean hindcast[END_REF] and is summarized below.

Ensemble Simulation Strategy

All members of the ensemble simulation were initialized using the final state of a common 21-year spin-up. We then introduced slight stochastic perturbations within each ensemble member during 1960 (see [START_REF] Brankart | Impact of uncertainties in the horizontal density gradient upon low resolution global ocean modelling[END_REF][START_REF] Bessières | Development of a probabilistic ocean modelling system based on NEMO 3.5: application at eddying resolution[END_REF], switched off these perturbations at the end of 1960, and resumed the integration of the 50 members until 2015 using the same fully varying DFS5.2 forcing. Nonlinear ocean dynamics yield an initial growth of incipient perturbations, i.e., of chaotic mesoscale anomalies; the subsequent ensemble spread then approximately saturates in amplitude within a few months or years depending on the region (see [START_REF] Zanna | Uncertainty and scale interactions in ocean ensembles: from seasonal forecasts to multi-decadal climate predictions[END_REF]. Nonlinear processes (e.g., eddy-eddy interactions, subsequent spatial and temporal inverse cascades) then contribute to extend the range of chaotic fluctuations toward lower wavenumbers and frequencies, hence feeding the LFCIV and larger structures which emerge around the ensemble mean within each member with a random phase. As shown in [START_REF] Sérazin | Quantifying uncertainties on regional sea-level rise induced by multi-decadal oceanic intrinsic variability[END_REF] under seasonal forcing, and in [START_REF] Sérazin | A global probabilistic study of the ocean heat content low-frequency variability: atmospheric forcing versus oceanic chaos[END_REF] and in [START_REF] Llovel | Contributions of atmospheric forcing and chaotic ocean variability to regional sea level trends over 1993-2015[END_REF] in the OCCIPUT ensemble, the LFCIV exerts an influence on decadal and longer periods as the OCCIPUT simulation proceeds, and leaves regional imprints on long-term trends in the form of random trends within each member. The present paper will assess whether (coastal) sea-level trends are also impacted by this random signal.

Computing Regional Sea-Level Trends

The full details of the post-processing are presented in [START_REF] Llovel | Contributions of atmospheric forcing and chaotic ocean variability to regional sea level trends over 1993-2015[END_REF] and summarized below. The diagnostics performed in this study started in 1993, i.e., after 21 + 34 = 55 years of dynamical adjustment within each member. At every grid point of each ensemble member, we first compute the linear trend of sea level over the 23-year period 1993-2015. The imprint of the model numerical drift on sea-level trends is then estimated from the climatological run in a similar way: the drift-related linear sea-level trend is computed at every grid point from the climatological run after 55 years of adjustment, i.e., between years 56 and 78. This field is removed from the trends of the 50 ensemble members to retain the geophysical sea-level trend signals. Finally, we subtract the global average from these 50 sea-level trend fields (this being necessary in Boussinesq ocean models, see [START_REF] Greatbatch | A note on the representation of steric sea level in models that conserve volume rather than mass[END_REF], yielding 50 estimates of regional sea-level trends over 1993-2015, corrected for the model drift and relative to their global average. These processing steps yield a remarkably small root-mean-square difference between observed and ensemble mean sea-level trends (1.57 mm/year over the period 1993-2015, see [START_REF] Llovel | Contributions of atmospheric forcing and chaotic ocean variability to regional sea level trends over 1993-2015[END_REF].

Consistently with the above, steric sea-level fields are calculated from the monthly 3-dimensional temperature and salinity fields archived from the 50 ensemble members (between 1993 and 2015) at every grid point. We estimate the spurious drift of 3-D temperature and salinity from the climatological run (between years 56 and 78), remove this drift from the 3-D temperature and salinity fields from the 50 members, compute the full-depth steric sea-level trend fields, and finally remove their respective global averages. This yields 50 regional steric sea-level trend fields, corrected for the model drift and relative to their global average. Manometric sea-level trends are computed from each ensemble member as the difference between sea-level trends and full-depth steric sea-level trends. Note that manometric sea-level trends refer to the ocean bottom pressure term in regional sea-level changes (see [START_REF] Gregory | Concepts and terminology for sea level: mean, variability and change, both local and global[END_REF] for more details).

The observed regional sea-level trend field is calculated over the same 1993-2015 period from the Climate Change Initiative (CCI, [START_REF] Legeais | An improved and homogeneous altimeter sea level record from the ESA Climate Change Initiative[END_REF]) dataset derived from several altimeter missions. The observed regional sea-level trend field is finally obtained by removing the global average from the latter field and used to assess the realism of the ensemble simulation.

Ensemble Statistics: Forced and Random Trends

The ensemble standard deviation (ESTD) of any oceanic field simulated with this initial perturbation ensemble modeling strategy quantifies the imprint of the chaotic variability on this field (i.e., the width of the ensemble spread). The ensemble mean (EMEAN) of any field provides an estimate of the atmospherically forced signal, since all members were driven by the same atmospheric forcing. For the purpose of this study, we estimated the forced sea-level trend (due to external influences, i.e., atmospheric variability and trend, anthropogenic influences, etc.) by the ensemble mean of the 50 sea-level trend maps, and the imprint of low-frequency chaotic variability by the ensemble standard deviation of these maps (which will quantify the amplitude of random trends in the following). These forced and random signals are estimated for the total, steric, and manometric regional sealevel trends. Using the Lilliefors test, we verified that local ensemble distributions of total and steric sea-level trend fields are Gaussian at the 95% significance level over 93% of the global ocean area. The use of EMEANs and ESTDs to estimate the forced and random trends is therefore adequate for our analysis.

Results from the 1/4° OCCIPUT Ensemble Simulation

Section 3.1 describes and compares the forced and random sea-level trends in the open ocean and summarizes the more detailed analysis presented by [START_REF] Llovel | Contributions of atmospheric forcing and chaotic ocean variability to regional sea level trends over 1993-2015[END_REF]. The focus is put on coastal regions in the following sections.

Forced and Random Regional Sea-Level Trends in the Open Ocean

Figure 1a, b shows the regional trends of sea level over the period 1993-2015 from altimeter observations and from a randomly picked OCCIPUT member (member #1), respectively. While some discrepancies are visible in certain regions (in particular in the North Atlantic western Subpolar Gyre), the distribution and magnitude of regional sealevel trends are quite well reproduced by the model: [START_REF] Llovel | Contributions of atmospheric forcing and chaotic ocean variability to regional sea level trends over 1993-2015[END_REF] show that the root-mean-square difference between OCCIPUT and observed trends is smaller than any simulation considered in [START_REF] Griffies | An assessment of global and regional sea level for years 1993-2007 in a suite of interannual CORE-II simulations[END_REF]. Large-scale patterns of regional sea-level trends range between roughly -3 and + 3 mm/year, and are found at similar locations in the model and the real ocean: large positive trends throughout most of the western Pacific and within the subtropical gyres of the South Indian, South Atlantic, and North Atlantic oceans; large negative trends over most of the eastern and southern Pacific, and along the Gulf Stream path.

We now take advantage of the information from the 50 members and split the simulated sea-level trends into their forced (EMEAN, Fig. 1c) and random (ESTD, Fig. 1d) components. The main large-scale patterns of regional sea-level trends simulated in member #1 happen to belong to the forced component over many regions (compare panels b and c); there indeed, random trends (panel d) remain smaller than about 1 mm/ year, i.e., smaller than forced trends. The relative contributions of forced and random trends should, however, be compared more quantitatively to identify regions where the "signal," associated with the atmospheric fluctuations and climate change, can be considered as significantly larger than the "noise," associated with LFCIV.

We define at every grid point a signal-to-noise ratio (SNR) as the ratio of the absolute value of the forced sea-level trend to the random sea-level trend, respectively, given by the EMEAN and ESTD of local trends. The larger the SNR, the more confidently one can attribute the regional sea-level trend found in one particular realization (i.e., one ensemble member picked randomly) to the external forcing, whether it be natural atmospheric variability or anthropogenic influences. Conversely, the smaller the SNR the more the low-frequency chaotic variability impacts the sea-level trends in a given realization, with a smaller impact of external sources. As Sérazin et al. (2017, their section 4), we consider that one may attribute the regional trend found in a given realization to the external forcing where SNR > 2, while one cannot unambiguously do so where SNR < 2 (at the 95% confidence level). In other words, regional sea-level trends in regions where SNR < 2 may just be random since they emerge from the LFCIV.

Figure 2 shows the global distribution of the sea-level trend SNR, and the black contour encircles regions where SNR < 2. Large forced trends are generally associated with large SNRs in vast areas of the intertropical Pacific, within most of the Eastern Pacific and Arctic oceans. This is no longer the case in many other parts of the global ocean: SNR < 2 over most of the South Atlantic (25-55°S), central and tropical parts of the North Atlantic (15-45°N, 0-10°N), western North Pacific (18-50°N, west of 180°W), western Indian ocean (west of 60°E, from 15°S to the northern boundary), and almost everywhere in the Antarctic Circumpolar Current (except in the South Pacific sector). There, our results suggest that regional sea-level trends are not certainly driven by external (atmospheric or anthropogenic) causes, but may be random since they are influenced by the intrinsic oceanic "noise" (LFCIV). In other words, sea-level trends in such regions are affected by a sizeable uncertainty due to chaotic ocean dynamics.

Forced and Random Regional Sea-Level Trends in Coastal Regions

Figure 2 shows that the SNR increases and passes the SNR = 2 threshold when approaching the coast in several regions, such as around Alaska, Antarctica, Australia and all islands located north of it, around all islands from Cuba to the lesser Antilles, or along the west coasts of America, Europe, and North Africa. Figure 3d shows that the coasts surrounding the southern tip of Africa (SA region) seem to be shielded from the very small SNR values found offshore within the strongly chaotic Agulhas Retroflexion. Along other coastlines, however, the opposite holds: the other panels of Fig. 3 show that over large coastal parts of the northwestern Pacific (NWP), western Indian Fig. 2 Ratio between the forced and random 1993-2015 regional sea-level trends (i.e., ensemble mean divided by the ensemble standard deviation, or signal-to-noise ratio) deduced from the OCCIPUT ensemble simulation. Sea-level trends found in a single member cannot be unambiguously attributed to the atmospheric forcing (95% confidence interval) in regions enclosed by the SNR = 2 isocontour (black) (WI), Gulf of Mexico, and US east coast (MEX), the SNR remains smaller than 2 and may even fall below 0.5 locally. In the latter coastal regions, the modeled sea-level trends may thus be random and cannot be unambiguously attributed to the atmospheric (and anthropogenic) forcing.

We now try to identify generic differences between the open ocean and coastal regions in terms of forced and random sea-level trends (and/or their ratio, SNR). We will focus on five specific domains: the global ocean, and the four domains shown in Fig. 3. We will show the distributions of forced trends, random trends, and SNR considering all grid points of each specific domain, then considering two subregions within each specific domain: the coastal domain (CD) will include all grid points located less than 25 km away from the coastline, whether they be deep or shallow. In a complementary way, the shallow domain (SD) will include all grid points where depth is shallower than 25 m, whether they be close to or far away from the coasts.

Scale of the global ocean

Let us first consider the global ocean domain. We sort in increasing order the signals (i.e., the absolute value of the forced sea-level trends) simulated at each grid point of the domain; we accumulate the areas of the corresponding grid points and express the result as a fraction (in %) of the total area of the domain. This result is shown in black in Fig. 4a (the fractional area is not shown for very small values of the signal): this line indicates for instance that the absolute value of forced sea-level trends is smaller than 0.4 mm/year over 20% of the global ocean area, smaller than 1 mm/year (the median) over half of it, larger than 3 mm/year over 10% of it, and does not exceed 50 mm/year anywhere. The same computation is done in the CD and SD subregions of the global ocean, and the results are shown in red and blue in the same figure. The differences between these 3 lines are generally small (median values are around 1 mm/year in the 3 regions), except for the largest signals: the signal exceeds 3 mm/year within only 5% of the area of CD, and barely anywhere in SD. We thus conclude that at global scale, the distribution of forced sea-level trends in shallow and coastal regions is comparable to their counterparts in the open ocean, except for extreme (and rare) signals which are much smaller near the coast.

The same three computations are repeated in the global ocean, substituting the signal with the noise (i.e., random trends or ensemble standard deviation). Figure 4b shows that noise values range between about 0.035 and 20 mm/year at global scale, with a median of 0.3-0.4 mm/year, that is 30-40% of the median of the signal. Unlike the signal however, the noise substantially decreases (by a factor of about 3 for the median, 10 for the maximum) when focusing on shallow (SD) and coastal (CD) domains. This reduction might be explained by one or several of the following hypotheses: the mesoscale processes that emerge and may locally feed LFCIV may be marginally resolved by the model since internal deformation radii are smaller in shallow regions (see, e.g., Hallberg 2013); the timescales of the LFCIV generated in these regions may not reach multiple decades and have less imprint on long-term trends; the multi-decadal LFCIV present in the neighboring open ocean may be high-pass filtered when approaching the coasts and shallow waters. Other hypotheses might exist, and further work is required to explain these features, which nevertheless are quite robust according to Fig. 4b.

Figure 4c does not show the ratio of the lines in the previous two panels, but presents the result of the binning described above applied to local SNR values within the global ocean, and its CD and SD subdomains. The black line shows that sea-level trends can be considered to be dominantly driven by the atmosphere over more than half (62%) of the global open ocean area (where SNR > 2). Colored lines show that regional sea-level trends in coastal and shallow parts of the global ocean are characterized by larger SNR values than in the open ocean: the SNR remains larger than 2 in about 80-83% of their area; the coastal areas are also those where the largest values of the SNR may be found at global scale.

These model results conversely show that within 17-20% of the coastal and shallow areas of the global ocean, the 1993-2015 sea-level trends are likely to be random because of LFCIV and are not certainly forced by external drivers. This proportion decreases from 38 to 17-20% from the open ocean to the shallow and coastal domains because the imprint of LFCIV on sea-level trends significantly decreases there. In other words, the model suggests that the attribution of observed sea-level trends (from altimetry or from tide gauges) to non-oceanic sources is questionable over 38% of the global ocean area, and over about one-fifth of the coastal and shallow water area. The implications of these results are further discussed in the last section of this paper.

Zoom on Four Specific Regions

We now describe in more detail the respective imprints of the external forcing and of the oceanic chaos on sea-level trends in the four regional domains shown in Fig. 3, and in their coastal (CD) and shallow (SD) parts.

We saw that coastal SNR values tend to remain small in the region surrounding the Southern tip of Africa (SA, Fig. 3d). Figure 5d shows that the SNR changes from the whole SA domain to its shallow and coastal parts are comparable to those described at global scale (Fig. 4c): while SNR values are smaller than 2 over most (62%) of the SA full domain, this proportion sharply decreases (17-23%) near the coasts and in shallow areas, except along the northeastern coasts of South Africa and the southeastern coast of Mozambique where the SNR remains smaller than 2 (and even less locally, see Fig. 3d). As in the global ocean, the decrease of SNR values in the coastal and shallow areas of the SA domain is essentially due to a sixfold decrease of the median (and more than a tenfold decrease of the maximum) of the LFCIV-induced noise, while the median of the signal remains very close to 1 mm/year (not shown). These resemblances suggest that in several parts of the global ocean, approaching the coastal and shallow oceans has comparable impacts on the forced and random parts of sea-level trends as in the SA region.

Figure 5b resembles Fig. 5d: within the whole region shown in Fig. 3b, SNR values are smaller than 2 over 62% of model grid points, and over substantially less (36-38%) grid points in its coastal and shallow parts, with a strong spatial inhomogeneity: coastal sea-level trends can be attributed to the forcing along most of US Atlantic coast (SNR > 2 from around Titusville, FL, to Nova Scotia at least) and along the coasts of the Caribbean islands. In contrast, our results suggest that coastal sea-level trends may be random over most of the Gulf of Mexico coastline (from southwest Florida to the southernmost point of the Gulf), with SNR values remaining even smaller than 0.5 everywhere between Pensacola, FL, to Caillou Bay, LO.

The structure of the forced and random trends is much more homogeneous along the coasts of the northwestern Pacific (NWP) domain, host of the strongly turbulent Kuroshio. Here as well, the SNR remains below 2 within most (about 68%) of its total area. In contrast with the other regions considered, however, this fractional area remains as large when only coastal regions are considered, and even increases (90%) in the shallow parts of the NWP domain. Figure 3a further shows that the sea-level trend SNR remains smaller than 2 (and becomes locally much smaller) almost everywhere along the continental and island coastlines located within the East China Sea, Yellow Sea, and Japan Sea, all the way between the cities of Haikou (South China) and Vladivostok, including most Japanese coastlines (except southern and northeastern Hokkaido). Further analysis in the NWP region (not shown) shows that the median forced sea-level trends now decrease by a factor 4-6 near the coasts and in shallow waters compared to the open ocean, while the imprint of LFCIV on these trends only decreases by a factor of 3, yielding these small SNR values over most of the coasts in this area. The NWP domain is therefore the region of the global ocean where attributing coastal sea-level trends to external drivers is the most questionable.

Steric and Manometric Contributions to the Coastal Sea-Level Trend Components

The total regional sea-level trends discussed above may be split in two components: steric trends result from the thermal expansion and haline contraction of seawater, and manometric (i.e., non-steric) sea-level trends come from local changes in the mass of seawater at each location. Note that the trends in the melting rate of glaciers and ice sheets are not taken into account in these simulations.

In this section, we investigate the respective imprints of steric and manometric components on the forced and random trends over the global ocean area, and in its shallow (SD), and coastal (CD) parts. Table 1 summarizes for each of these three domains the forced part, the random part, and the SNR of the total, steric and manometric regional sea-level trends. The last three lines in Table 1 are derived from the counterparts of Fig. 4 drawn for the steric and manometric sea-level trends (not shown); colors correspond to the whole global ocean, its coastal and shallow parts.

Steric and Manometric Coastal Sea-Level Trends: Forced Part

The second line in Table 1 concerns the median of the absolute value of the signal (i.e., of the forced trends). In Fig. 4a, this median corresponds to the abscissae where each line reaches the 50% fractional area. As explained in the previous section, the median absolute values of the forced total sea-level trends are basically the same over the open ocean, the coastal and shallow domains (close to 1 mm/year, see line 2, column 2). The next two columns of line 2 further indicate that forced steric trends are also typically close to 1 mm/ year in absolute value over these 3 domains, but that forced manometric trends (last column) are 4 and 10 times stronger in the coastal and shallow domains, respectively. This strong increase of forced manometric trends toward the coast is consistent with several studies using forced ocean circulation models [START_REF] Griffies | Physical processes that impact the evolution of global mean sea level in ocean climate models[END_REF]) and coupled climate models (Landerer et al. 2007a, b;[START_REF] Yin | Model projections of rapid sea-level rise on the northeast coast of the United States[END_REF][START_REF] Yin | Spatial variability of sea-level rise in 21 st century projections[END_REF] at coarse resolution. Sea-level projections in the late twenty-first century show an increase of bottom pressure loading along shelves and marginal seas related to the expansion of open ocean water due to the increased concentration of greenhouse gases in the atmosphere. Such a forced increase of ocean heat content in the open ocean may create a steric sea-level gradient next to the continental shelf and push water masses toward the coast at the shelf break. As the deep open ocean can absorb more heat than shallower coastal regions, steric sea-level trends can be greater away from the coastal zone. Therefore, the steric sea-level change yields a dynamic topography gradient near the continental shelf areas, with lower dynamic topography on the shelves than in the open oceans. Dynamic topography gradients may then locally modify ocean currents through dynamical adjustments. Therefore, open ocean water is expected to progressively penetrate on the shelves, increase mass and therefore ocean bottom pressure in the coastal areas, yielding this enhanced forced manometric sealevel trend near the coasts.

Steric and Manometric Coastal Sea-Level Trends: Random Part

The third line in Table 1 concerns the median of the noise (random trends). In Fig. 4b, this median corresponds to the abscissae where each line reaches 50% fractional area. As mentioned in Sect. 3.2.1, the median amplitude of random total sea-level trends is close to 0.3 mm/year over the whole global ocean area, i.e., about 30% of the typical forced signal. Unlike the forced (total and steric) sea-level trends which were similar in the whole, coastal and shallow regions, typical values of their random counterparts drop by 70-99% when only coastal and shallow domains are considered (columns 2 and 3, line 3).

As was noted for its forced counterpart, the manometric random sea-level trend median increases (roughly doubles) from the open ocean to its coastal and shallow parts, and gets similar as the total random trend median (about 0.1 mm/year). This amplification toward the coasts of manometric trends thus concerns both the forced and random components, unlike the steric trends whose medians remain unchanged (forced component) or sharply drop (random component). The dynamical hypotheses presented in Sect. 3.3.1 to explain the coastal amplification of forced manometric trends are likely to hold for their random counterparts.

Steric and Manometric Coastal Sea-Level Trends: Signal-to-Noise Ratio

The reader might have noted that adding the medians of steric and manometric sea-level trends (columns 3 and 4 in lines 2 or 3) does not yield the median of total sea-level trends (column 2). Indeed, the fractional areas corresponding to steric and manometric components are computed independently after sorting their values by increasing order. In other words, the values given in rows 2 and 3 of Table 1 do not take into account the possibility of local compensations between steric and manometric signals. These possible compensations are now taken into account: the last line of the table gives the fraction of the area of the global ocean (full, coastal, and shallow domains) where the local signal-to-noise ratios (SNR) of total, steric, and manometric sea-level trends are smaller than 2. This is the percentage of the area where regional trends cannot be unambiguously attributed to external causes (95% confidence), but may be due to the LFCIV.

As mentioned earlier, attributing total sea-level trends to the atmospheric forcing is questionable over 38% of the global ocean area; this fraction decreases to 17-20% in its coastal and shallow parts (line 4, column 2). The changes of the forced and random parts of the steric and manometric signals when approaching the coast (described above separately) combine together when considering them locally, and yield a simpler picture in terms of SNR: the fractional area over which the oceanic LFCIV may affect the (steric, manometric, and total) sea-level trends consistently decrease when switching from the global ocean to its coastal and shallow parts. In the coastal regions located within 25 km of the coasts, the external forcing cannot be certainly held as the main driver of total sea-level trends over 17% of the oceanic area. This area proportion is slightly larger (30%) for manometric sea-level trends, and clearly smaller for steric sealevel trends (5%).

In summary, our results show that sea-level trends in coastal regions are somewhat shielded from the LFCIV, whose relative contribution compared to the forced signal is smaller than in the open ocean. The attribution of coastal sea-level trends to external forcing (atmospheric fluctuations, anthropogenic forcing) is thus valid over most of the globe, but requires care in regions where the SNR approaches 2, and may be invalid where SNR values drop below this level (i.e., within 17-20% of the global ocean coastal area). The model suggests that sea-level trends in such regions may be random since they are substantially impacted by the ocean-driven low-frequency chaotic variability.

Conclusions and Discussion

Sea-level trends have a complex distribution along the coasts, where the ongoing global mean sea-level rise can be either enhanced or reduced. The accurate monitoring and understanding of these coastal trends requires detailed analyses of their causes, and of the associated uncertainties. In this paper, we investigated the contributions of two drivers of coastal sea-level trends over the altimetric period : the trends driven by the atmospheric evolution (of natural or anthropic origin), and the trends driven by the oceanic Low-Frequency Chaotic Intrinsic Variability (LFCIV). The latter driver is substantial when mesoscale eddies are (even partly) resolved, and should be considered as a source of uncertainty for attributing coastal sea-level trends to external drivers: the LFCIV indeed induces random fluctuations on sea-level trends and other oceanic fields.

Using the outputs of a large ensemble of 1/4° global oceanic hindcasts, we showed that, in certain coastal areas, this "noise" may blur the detection of regional sea-level trends.

Our results do not concern (and do not question the anthropic origin of) the globally averaged 1993-2015 sea-level trend, which was removed from our datasets: they concern the regional contrasts of sea-level trends near the coasts, specifically their external or internal origin. Our main results may be summarized as follows:

• Coastal sea-level trends are not significantly impacted by the ocean-driven multi-decadal LFCIV over most (80-83%) of the global ocean area located less than 25 km away from the coasts. They may be attributed to non-oceanic (atmospheric or anthropic) causes with 95% confidence level. • However, coastal sea-level trends cannot be unambiguously attributed to atmospheric drivers over the remaining 17-20% of the global ocean coastal area. There, the oceandriven multi-decadal LFCIV is smaller than in the open ocean, but still induces random sea-level trends that represent more than half of the externally driven counterpart, and may blur the detection of the latter. • These latter regions are inhomogeneously distributed around the globe and sit near strong eddy-active regions (Fig. 3). They include in particular all island and continental coastlines between 142°E and the Asian coast between 20 and 42°N, most of the Gulf of Mexico coastline, and several parts of the northwestern Indian Ocean coastlines. These results suggest that the presently available 23-year altimeter record is not long enough to rigorously assess the externally forced character of sea-level trends along 17-20% of the coastlines. It is nevertheless likely that a longer altimetric record will progressively increase the percentage of coastal areas where the LFCIV does not perturb the attribution of sea-level changes. In this context, an interesting perspective of this study would be to assess the contribution of atmospherically forced and internally generated sealevel trends in coastal regions where (longer) tide gauge records are available.

The members of this ensemble simulation represent the observed distribution of regional sea-level trends with a very good degree of accuracy in the open ocean (as quantified in [START_REF] Llovel | Contributions of atmospheric forcing and chaotic ocean variability to regional sea level trends over 1993-2015[END_REF], except in a few areas such as the western Subpolar Gyre of the North Atlantic. As for any model-based study however, our results should be considered with caution. The fidelity of 1/4° simulations may decrease from the open ocean toward the coasts: certain coastal processes are either absent from our model (e.g., tides, surface gravity waves, etc.), or may be marginally resolved (mesoscale turbulence, edge waves, coastal wind drop-off, certain upwellings, etc.) since depth, hence the internal Rossby radii and the model effective resolution, generally decrease when approaching the coasts. Future investigations of forced and random coastal sea-level trends could utilize for instance higher resolution ensembles of regional coastal simulations (with adequate lateral forcing), and ideally ensembles gathering different types of models. The present study may in any case be seen as a proof of concept: it illustrates at least the potential of ensemble-based modeling strategies for disentangling internal and external sources of oceanic fluctuations over a wide range of scales.

As noted in Sect. 1.2, the ocean-driven LFCIV, and therefore random sea-level trends, are largely underestimated in laminar ocean simulations forced by the atmosphere, and presumably also in ocean-atmosphere coupled simulations where the oceanic mesoscale is absent. In other words, the LFCIV is an oceanic driver of coastal sea-level changes in the turbulent regime, which may compete with the external drivers examined in [START_REF] Woodworth | Forcing factors affecting sea level changes at the coast[END_REF] and with the ocean-atmosphere coupled modes presented by [START_REF] Han | Impacts of basin-scale climate modes on coastal sea level: a review[END_REF]. More importantly, the random character of LFCIV suggests that it actually constitutes a source of uncertainty for the detection and attribution of coastal sea-level trends, in addition to those simulated by climate models [START_REF] Carson | Climate model uncertainty and trend detection in regional sea level projections: a review[END_REF], and that these uncertainties should also be taken into account for coastal sea-level projections (see [START_REF] Jevrejeva | Probabilistic sea level projections at the coast by 2100[END_REF]. [START_REF] Fasullo | Altimeter-era emergence of the patterns of forced sea-level rise in climate models and implications for the future[END_REF] and [START_REF] Hamlington | Uncovering the pattern of forced sea level rise in the satellite altimeter record[END_REF] used ocean-atmosphere coupled ensemble simulations (with a non-eddying ocean component) to extract the "internal" and "forced" sea-level trends. In their context however, (1) "internal" refers to the variability (e.g., ENSO, PDO, etc.) and trends that emerge from the air-sea coupling and in the turbulent atmosphere, whose phase are essentially random and differ among ensemble members; (2) and "forced" refers to the response of the coupled system to the sole anthropogenic forcing (greenhouse gases concentration increase in particular).

In our study, we have used an ocean-only ensemble simulation (with an eddying ocean model) driven by a prescribed atmospheric variability. As explained in Sérazin et al. (2017, their introduction) and in [START_REF] Penduff | Chaotic variability of ocean: heat content climate-relevant features and observational implications[END_REF], this prescription of the atmospheric variability is mandatory to split the oceanic variability into its atmospherically forced component, and its intrinsic/chaotic variability that spontaneously arises in the turbulent ocean. In other words, what we called the "forced" ocean variability and trends are those driven by the atmospheric forcing (including the anthropogenic trends it contains), and what we called the LFCIV and the random trends emerge in the ocean from nonlinear processes without coupling to the atmosphere. It is important to recall, as mentioned in Sect. 1.2, that this oceanic LFCIV is very small in non-eddying ocean models [START_REF] Penduff | Sea-level expression of intrinsic and forced ocean variabilities at interannual time scales[END_REF][START_REF] Grégorio | Intrinsic variability of the Atlantic meridional overturning circulation at interannual-to-multidecadal time scales[END_REF]: [START_REF] Fasullo | Altimeter-era emergence of the patterns of forced sea-level rise in climate models and implications for the future[END_REF] and [START_REF] Hamlington | Uncovering the pattern of forced sea level rise in the satellite altimeter record[END_REF]'s coupled simulations performed with a non-eddying ocean are thus certainly underestimating this chaotic variability that our eddying ocean model generates. In other words, the processes and signals that we have disentangled are distinct from those considered in the latter two studies.

Characterizing the imprints of LFCIV on, e.g., sea-level trends in a global eddying 50-member ensemble simulation coupled to the atmosphere would not only require huge computational resources; it would also require simulation and analysis strategies allowing to separate intrinsic and forced signals within two fluids in complex interaction, and such strategies are not clear yet. An intermediate step could consist of forcing atmospheric model ensembles with sea-surface temperature (or upper ocean heat content) fields simulated in several OCCIPUT members. This would help to answer important but open questions about the atmospheric response to random trends of the upper ocean heat content [START_REF] Sérazin | A global probabilistic study of the ocean heat content low-frequency variability: atmospheric forcing versus oceanic chaos[END_REF], which contribute to the steric sea-level trends discussed here. These ambitious modeling and physical objectives are left for the future.

project from ESA Living Planet Fellowship fundings. The CCI product is freely available at http://www. esa-seale vel-cci.org/. The model dataset used for this study is freely available on http://zenod o.org (http:// doi.org/10.5281/zenod o.14879 83). We would like to thank two anonymous reviewers for their constructive comments and helpful suggestions.

Fig. 1

 1 Fig. 1 1993-2015 regional sea-level trends from the CCI observational product (a) and from the OCCIPUT ensemble simulation: ensemble member #1 (b), forced trends (c, ensemble mean), and random trends (d, ensemble standard deviation)

Fig. 3

 3 Fig. 3 Zooms of Fig. 2 in the Northwest Pacific (a), the Northwest Atlantic (b), the Northwest Indian (c), and around the south of Africa

Fig. 4

 4 Fig. 4 Cumulative fractional area of the global ocean as a function of: a absolute value of the forced sealevel trends; b random sea-level trends; c local signal-to-noise ratio shown in Fig. 2. Black lines show the results for all model points, red lines for model points located within 0-25 km from the coasts, blue lines for model points located in regions shallower than 25 m

Fig. 5

 5 Fig. 5 Same as Fig. 4c for the four domains shown in Fig. 3 (with identically laid out panels)

Table 1

 1 Main statistics (last 3 lines) of total, steric, and manometric sea-level trends (last three columns) over the global ocean: whole domain (black), grid points within 25 km of the coasts (red), grid points with depth shallower than 25 m (blue)

	qLOBAL CEAN¡		Total			Steric		Manometric
		sea level trends	sea level trends	sea level trends
	Whole Coastal Shallow
	Median of	1.0	1.0	1.0	1.0	0.9	0.9	0.1	0.4	1.0
	the Signal Absolute value
	(Forced sea level trends,
	mm/yr)
	Median of the Noise	0.3	0.1	0.1	0.3 0.045 0.025 0.05 0.09 0.1
	(Random sea level trends,
	mm/yr)
	Fractional area where S/R < 2 38% 17% 20% 37% 5%	1%	56% 30% 14%

  • Steric sea-level trends are impacted by LFCIV over only 5% of the global ocean coastal area; manometric sea-level trends are impacted by LFCIV over a larger fraction (30%) of it.

That is, a simulation driven by an atmospheric reanalysis, i.e., including the full range of timescales.

Certain 1°-resolution simulations produce LFCIV, albeit with much weaker intensity (e.g., O'Kane et al. 2013).

Although other processes such as large-scale baroclinic instability may also produce LFCIV[START_REF] Huck | Multidecadal variability of the overturning circulation in presence of eddy turbulence[END_REF].

Acknowledgements This work is a contribution to the OCCIPUT and PIRATE projects. PIRATE (https :// seale vel.jpl.nasa.gov/scien ce/ostsc ience team/scien tistl inks/scien tific inves tigat ions2 017/pendu ff/) is funded by CNES through the Ocean Surface Topography Science Team (OST-ST). OCCIPUT (https ://meom-group .githu b.io/proje cts/occip ut/) was funded by ANR through contract ANR-13-BS06-0007-01. This work was also supported by the French national program LEFE/INSU and has received funding from the European Union Horizon 2020 research and innovation program under grant agreement No 633211. It is also part of the Copernicus Marine Environment Monitoring Service (CMEMS) GLO-HR project; CMEMS is implemented by Mercator Ocean International in the framework of a delegation agreement with the European Union. We acknowledge that the results of this research have been achieved using the PRACE Research Infrastructure resource CURIE based in France at TGCC. William Llovel was supported by C3S program, "Louis Gentil-Jacques Bourcart" fellowship from the French Académie des Sciences and by the OVALIE


it underwent successive reforms. This policy brief shows that the short-time work reforms carried out after the recession have mainly benefited large firms using them on a regular basis to cope with seasonal fluctuations in business activity. This expansion of short-time work is inefficient because it subsidizes periods of inactivity, thus reducing total output. In this context, it would be desirable to introduce a bonus-malus system by which companies would fund short-time work via a tax paid over several years and that is proportional to their contribution to the cost of the scheme.

•

The growth of the short-time work scheme since 2008 has primarily benefited large companies using it on a regular basis to cope with seasonal fluctuations in business activity.

• These subsidies to companies facing strong seasonal fluctuations at the expense of the rest of the economy result in a decrease in total output.

•

The introduction of a bonus-malus system, within which companies would fund short-time work via a tax paid over several years and that is proportional to their contribution to the cost of this scheme, would make this policy more effective.

(1) CREST-ENSAE-Ecole Polytechnique (2) Banque de France. The opinions expressed in this IPP policy brief are those of the authors and cannot be attributed to the Banque de France or Eurosystem. However, despite these windfall effects, some countries decided to retain their short-time work scheme after the recession. In France, since 2008, under pressure from companies that most rely on short-time work, the public authorities have decided to make the short-time work scheme more generous, which has contributed to a considerable expansion of the scheme. This policy brief shows that this expansion has mainly benefited large companies that use it on a regular basis to cope with seasonal fluctuations in business activity. This situation is inefficient because it subsidizes companies and sectors with high seasonal fluctuations at the expense of the rest of the economy. These cross-subsidies reduce overall production. In this context, the introduction of a bonus-malus system, within which companies would fund short-time work through a tax proportional to their contribution to the cost of this scheme, would make this policy more effective.

THE SHORT-TIME WORK SCHEME SINCE 1 JULY 2013

All companies subject to the Labour Code and all their employees are eligible for the short-time work scheme. Six grounds can justify its implementation: ( 1 Short-time work may be applied to all or part of the company and may take the form of an hourly reduction or a temporary suspension of employment. A company uses short-time work for its non-working hours of less than 35 hours per week (or the contractual or collective working time if this is less), for a maximum period of six months (which can be renewed in exchange for commitments), and for a maximum of 1,000 hours per employee per year.

For each hour taken off for short-time work, the company compensates the employee up to 70% of his or her previous gross hourly wage (100% if the employee is undergoing training). The company is then partially reimbursed by the government in the form of an hourly subsidy according to the size of the business: €7.74 for companies with 250 employees or less and €7.23 for companies with 251 employees or more.

THE SHORT-TIME WORK REFORMS OF 2012-2013

2 Field: Metropolitan France excluding Corsica; business sectors excluding agriculture; firms using short-time work for economic reasons. Note: "5 years" represents systematic users using short-time work every year over the last 5 years; "3 to 4 years" represents repeated users using short-time work 3 to 4 years over the last 5 years; "1 to 2 years" represents occasional users using short-time work 1 to 2 years over the last 5 years.

THE RISE OF SHORT-TIME WORK

Before the Great Recession of 2008-2009, short-time work was not widespread, and its budget fluctuated between €5 and 10 million per year. In 2009, in response to the economic recession, this budget amounted to €300 million. In 2012 and 2013, the reforms considerably increased the amount of the scheme's benefits, the cost of which was multiplied by 20 in 2013 compared with the period prior to 2009 (Figure 3).

Short-time work nevertheless plays a small role in the French economy as the scheme concerns less than 1% of companies and less than 0.5% of hours worked. However, the hours of short-time work are extremely concentrated within a small number of companies that use them on a regular basis. To understand this pattern, it is useful to distinguish three categories of companies:

After a report by three representatives of large companies and a senior civil servant 4 , and in response to requests made by professional organisations in the National Interprofessional Agreement (ANI) of 13 January 2012, the public authorities reformed the short-time work scheme.

Thus, in July 2013, the short-time work allowance was increased from 60% to 70% of the previous gross hourly wage and the hourly minimum of €6.84 was abolished. These reforms have also led to increases in the hourly short-time work subsidy, which was successively raised from €3.33/€3.84 to €4.33/€4.84 in March 2012 and to €7.74/€7.23 in July 2013 (Figure 1). Over the period as a whole, while employees in short-time work, most of whom are paid around the minimum wage, saw their hourly short-time work allowance maintained at their usual wage level, the company's cost for short-time work fell from 50% to 0% of the allowance between 2008 and 2013 due to the increase in the public subsidy (Figure 2). The top 1% of users, most of whom are systematic users, consumed more than 50% of the short-time work hours between 2006 and 2014. Most of the largest systematic consumers of short-time work are present over the entire 2008-2014 period. A high proportion of systematic users in 2008 also figures among the systematic users in 2014 and this proportion is even higher when the largest systematic users are considered (Table 1). The reforms of short-time work have therefore mainly benefited a small number of large firms that make massive regular use of the scheme in order to cope with their seasonal fluctuations in business activity.

THE INEFFICIENCY OF REGULAR SHORT-TIME WORK

In times of recession, short-time work offers companies facing temporary and financial difficulties the opportunity to retain their workforce. As such, short-time work generally helps to reduce job losses during a recession. However, short-time work does not have only advantages: it leads to a reduction in the number of hours worked per employee and it can subsidise enterprises that are insufficiently productive at a high cost to public finances.

Our recent research (Cahuc and Nevoux, 2017) shows that the current short-time work scheme in France is not adapted to protect employees and companies from seasonal fluctuations in activity. This measure relies exclusively on public funding. The absence of any contribution from user companies leads to overconsumption and regular use of short-time work. The model we are developing shows that the 2012-2013 reforms of short-time work have induced a financial transfer to enterprises that use shorttime work repeatedly and undergo significant seasonal fluctuations. However, these public subsidies, necessarily funded by other sectors and firms, result in production losses at the macroeconomic level insofar as they prevent the reallocation of labour experiencing seasonal fluctuations in business activity towards more productive sectors. We estimate that the aggregate production loss associated with the current short-time work scheme, compared to the social optimum, is equal to 50% of the total short-time work subsidy allocated to systematic users, i.e., around €40 million (Figure 4). In this context, unemployment insurance funded by contributions that increase for companies whose employees receive unemployment benefit is more effective. This bonus-malus for unemployment insurance encourages companies to internalise their redundancy costs and thus to keep their employees employed during periods of low activity. This unemployment insurance can usefully be supplemented by short-time work, so that firms facing temporary difficulties can retain their employees by reducing working hours. Funding of short-time work should however follow the same bonus-malus logic.

CONCLUSION: LIMIT THE REGULAR USE OF SHORT-TIME WORK

Our results highlight that short-time work schemes in which employers contribute little to their funding encourage firms faced with large seasonal fluctuations in their business activity to use them on a regular basis, thus reducing aggregate output. It is thus desirable to limit the regular use of short-time work. The introduction of a bonus-malus system, by which companies would fund short-time work in proportion to their financial involvement in the scheme, is one way of achieving this. The introduction of a bonus-malus for short-time work would however reduce its attractiveness and consequently lead to job losses. The current shorttime work scheme must therefore be supplemented by a bonus-malus for unemployment insurance in order to encourage companies facing temporary difficulties to retain their workforce and to fund unemployment benefits for employees who lose their jobs.

  .eu The Institut des Politiques Publiques (IPP) has been developed through a scientific partnership between the Paris School of Economics (PSE) and the Centre for Research in Economics and Statistics (CREST). IPP's aim is to promote quantitative analysis and evaluation of public policy using cuttingedge research methods in economics. Summary Short-time work makes it possible for companies faced with temporary and exceptional circumstances to receive subsidies to reduce the number of hours worked by their employees by remunerating the time off. Short-time work has both beneficial and detrimental effects. During the Great Recession of 2008-2009, there was renewed interest in short-time work as part of the fight against unemployment, particularly in France, where

  Short-time work is a means of safeguarding employment. It enables companies faced with temporary and exceptional circumstances to receive subsidies to reduce the number of hours worked by their employees by remunerating them for time off. Short-time work can have beneficial effects for employees, enterprises and public authorities. With it, employees keep their jobs and are assured a minimum income. The company reduces labour costs and preserves its human capital. By avoiding redundancies, short-time work also improves the social climate and can reduce unemployment insurance expenditure. However, short-time work also has detrimental effects. For reasons of profitability, financially viable companies may place certain employees on a part-time basis whom they would have retained full-time if no compensation were available. The scheme may be used by firms facing structural economic difficulties to subsidise jobs destined for elimination and whose employees would otherwise have been made redundant and possibly re-employed in more productive firms. During the Great Recession of 2008-2009, there was renewed interest in short-time work as a means to combat unemployment. Several countries, including Belgium, Turkey, Italy and Germany, have encouraged its use. Empirical research suggests that short-time work helped reduce unemployment during the recession. However, the positive effect of short-time work seems limited to periods of recession. In more favourable economic conditions, short-time work appears to lead to a drop in hours worked without any significant effect on employment 3 .

  ) Economic situation; (2) Modernisation, restructuring and transformation; (3) Problems in the supply of raw materials and energy; (4) Disaster; (5) Exceptional bad weather; (6) Other exceptional circumstances.

FIGURE 1 -

 1 FIGURE 1 -Hourly short-time work subsidy from 2002 to 2014.

FIGURE 2 -

 2 FIGURE 2 -Hourly cost of short-time work in 2008 and 2014.

  (i) occasional users using short-time work from 1 to 2 years in the last 5 years; (ii) repeated users using short-time work from 3 to 4 years in the last 5 years; (iii) systematic users using short-time work every year in the last 5 years. Regular use of short-time work by systematic users increased from 2 to 10 million hours between 2006 and 2014, representing more than 50% of total short-time work hours after the recession and accounting for more than half of public spending on the scheme in 2014 (Figure4).

FIGURE 3 -

 3 FIGURE 3 -Total short-time work subsidy and total number of short-time work hours from 2006 to 2014.

  hourly wage (in euros) Gross hourly wage (in euros)

  . and Nevoux, S. (2017). Inefficient short-time work. Discussion Paper 11010, Institute of Labor Economics (IZA).

Table 1 -

 1 Companies making regular use of short-time work in 2008 and 2014. : DADS (Insee), Sinapse (DGEFP) and Extranet (ASP). Field: Metropolitan France excluding Corsica; business sectors excluding agriculture; firms using short-time work for economic reasons. Note: There were 2,501 regular users in 2014.

		Proportion of
	regular users in 2008 486 244 49 SourcesNumber of Total Among the top 50% of users Among the top 10% of users Among the top 1% of users 5	regular users in 2008 who remain regular users in 2014 0.26 0.30 0.29 0.60


Mathieu Bourdeau

David Werner
email: dwerner@cameo-innovation.com

Philippe Basset

Elyes Nefzaoui
email: elyes.nefzaoui@esiee.fr

A sensor network for existing residential buildings indoor environment quality and energy consumption assessment and monitoring

Keywords: Sensor Network, Energy Monitoring, Building Energy Efficiency, Energy Retrofit

Enhancing residential buildings energy efficiency has become a critical goal to take up current challenges of human comfort, urbanization growth and the consequent energy consumption increase. In a context of integrated smart infrastructures, sensor networks offer a relevant solution to support building energy consumption monitoring, operation and prediction. The amount of accessible data with such networks also opens new prospects to better consider key parameters such as human behaviour and to lead to more efficient energy retrofit of existing buildings. However, sensor networks planning and implementation in general, and in existing buildings in particular, is a particularly complex task facing many challenges and affecting the performances of such a promising solution. In the present paper, we report on a field experiment of a sensor network deployment involving more than 250 sensors in three collective residential buildings in Paris region for the evaluation of a deep energy retrofit. More specifically, we describe the whole process of the sensor network design and roll-out and highlight the main critical aspects in such complex process. We also provide a feedback after several months of the sensor network operation and preliminary analysis of collected data. Reported results path the way for an efficient and optimized design and deployment of sensor networks for energy and indoor environment quality monitoring in existing buildings.

INTRODUCTION

Residential buildings are one of the major energy consumers and greenhouse gas (GHG) emitters, with 38.1% of the final energy consumption and 36% of the GHG emissions in Europe (ADEME, 2015). Efforts have been made to reduce the impact of residential buildings on energy consumption with various codes, standards and thermal regulation mandatory compliance for designs of new buildings (ASHRAE, 2013;HARMONIE, 2017). However, given the slow turnover of the building stock in European countries, the effect of these regulations is limited (INSEE, 2017). Hence, existing building retrofit turns into a priority (ADEME, 2018). On the other hand, ambitious massive smart sensor networks plans (European Commission, 2019;European Parliament & European Council, 2009;French Ministry of Ecological and Sustainable Transition, 2016) have been launched in recent years to enhance buildings energy efficiency.

Smart sensor networks have been largely deployed in buildings for energy monitoring and operation [START_REF] Bourdeau | Buildings energy consumption generation gap: A postoccupancy assessment in a case study of three higher education buildings[END_REF][START_REF] Fan | Unsupervised data analytics in mining big building operational data for energy efficiency enhancement: A review[END_REF] or building energy consumption forecasting [START_REF] Bourdeau | Modeling and forecasting building energy consumption: A review of datadriven techniques[END_REF][START_REF] Jain | Forecasting energy consumption of multifamily residential buildings using support vector regression: Investigating the impact of temporal and spatial monitoring granularity on performance accuracy[END_REF]. Studies have used sensors to highlight and characterize the link between energy efficiency and inhabitants' behaviour [START_REF] Li | Occupant Behavior and Building Performance[END_REF][START_REF] Menezes | Predicted vs. actual energy performance of non-domestic buildings: Using post-occupancy evaluation data to reduce the performance gap[END_REF][START_REF] Pisello | Human-based energy retrofits in residential buildings: A cost-effective alternative to traditional physical strategies[END_REF], identified as one of the main source of energy performance gaps [START_REF] De Wilde | The gap between predicted and measured energy performance of buildings: A framework for investigation[END_REF]. Data collection solutions have also been proposed to supervise building energy retrofits [START_REF] Ben | Energy retrofit and occupant behaviour in protected housing: A case study of the Brunswick Centre in London[END_REF][START_REF] Calì | Energy performance gap in refurbished German dwellings: Lesson learned from a field test[END_REF][START_REF] Cstb | ISABELE mesure la performance énergétique intrinsèque d[END_REF][START_REF] Jankovic | Lessons learnt from design, off-site construction and performance analysis of deep energy retrofit of residential buildings[END_REF]. However, instrumentation solutions deployment is a complex task, facing many challenges and difficulties. Thus, it directly impacts on the quality of the analyses and the efficiency of related energy savings measures [START_REF] Calì | Energy performance gap in refurbished German dwellings: Lesson learned from a field test[END_REF][START_REF] Jankovic | Lessons learnt from design, off-site construction and performance analysis of deep energy retrofit of residential buildings[END_REF][START_REF] Pisello | Human-based energy retrofits in residential buildings: A cost-effective alternative to traditional physical strategies[END_REF].

In this context, we present a feedback on a case study of a sensor network deployed in three existing collective residential buildings in France. The instrumentation takes part in a larger project that aims to study the impact of deep energy retrofit measures on the studied building energy consumption.

The present paper is organized as follows: we present the project case study in Section 2 ,then, we describe details of the instrumentation solution in Section 3. A feedback on the main critical points for sensor networks implementation in existing buildings is proposed in Section 4. Finally, Section 5 presents lessons learned from priliminary analysis of data collected after several months of operation of this experimental sensor network.

PRESENTATION OF THE CASE STUDY

In the present research project, a group of three existing social residential buildings -63 apartments over a 4,600 m² living areais considered for field experimentation. Buildings were built in 1974 in Paris (France) eastern suburb. Shared areas of the three buildings and a 10-apartment sample are instrumented for a period of three years, starting in March 2019. The ten apartments comprise surfaces from 50 to 75 m² distributed in the three studied buildings, on different floors and with different orientations. Apartment case studies have one to two occupants of various ages, professional occupation and living habits. For all three buildings, heating and domestic hot water are provided through a heating substation located in one of the three buildings and served by a neighborhood gas furnace. Thus, heating settings and management are centralized. All appliances in apartments are electric appliances excepted for those using natural gas for cooking.

Case studies only had minor retrofit actions. They are now planned to undergo deep energy retrofit measures over an eighteen-month period in 2020-2021. Retrofit measures will be implemented on occupied site with tenants living in their apartments during the whole retrofit period. Retrofit actions in shared areas include i) the removal of the heating substation and the connection to a local urban heating network, ii) exterior thermal insulation and iii) installation of a new controlled mechanical ventilation. In the apartments, it includes renewal of the iv) radiators and of v) the whole glazing system.

INSTRUMENTATION METHODOLOGY

Instrumentation plan

The instrumentation deployed aims to provide a multi-scale and multi-targets wireless monitoring solution. It focuses on data collection at both building-and apartment-scale for energy consumption, outdoor and indoor conditions, and inhabitants' comfort and behaviour. Moreover, the installed sensor network needs to be as non-intrusive as possible. This is essential to ensure that the participants' comfort and living habits remain undisturbed to prevent any bias in the experiment.

Sensor characteristics and deployment

The sensors selection and deployment are performed in two different phases, to set a total number of 259 sensors and connected objects (Table 1). The first deployment phase covers shared areas and entire building level. It involves only 10% of the total number of sensors for 35% of the total cost. In this phase, sensors provision, installation and data communication are entirely managed by a hired contractor. Electricity consumption is monitored on the main electricity meters and switchboards targeting the overall and detailed shared areas energy consumption (lightings, lifts and ventilation) with a one-minute time-step. Electricity consumption of water pumps in the heating substation is also monitored.

Building-scale thermal energy consumption is assessed using ultrasound thermal energy meters (Figure 1), with a five-minute timestep. Infrared presence detection sensors are positioned at the main entrance door of the three buildings and indoor temperature and humidity sensors are positioned on three floors of each building ground floor, middle and last floorfor data collection with hourly time-step. Finally, a weather station is positioned on a nearby university building to monitor local air temperature, humidity, wind speed, wind direction, rainfall and solar irradiation data at 5-minute time-step. This first instrumentation step is now fully operational, exception made for the weather station which is currently being installed.

The second part of the sensors focuses on the characterization of apartments (aside from buildingscale monitoring of domestic hot water consumption delayed to this second phase). Power demand is assessed with sensors installed on the main electric meter and switchboard, and smart-plugs to monitor all the main appliances of the instrumented apartments (one-minute time-step). Apartment-scale hot water consumption is assessed using contacttemperature sensors on hot water pipes (one-minute time-step) completed with data from already-installed remote reading volumetric meters. Also, heating energy consumption is deduced in a similar way using contact-temperature sensors on heaters (hourly timestep). Natural gas consumption, only used for cooking, is monitored with sensors installed on apartments gas meter (one-minute time-step). Indoor conditions and comfort should be captured using contact-temperature sensors positioned on exterior walls of the apartments and a sensor combining indoor temperature, humidity, luminosity, CO2 and presence measurements (hourly time-step). Finally, occupants' behaviours should mainly be characterized through occupation data and using sensors for window opening-closing detection. This second deployment phase will start in November 2019.

Communication network and online data collection

Data communication is mainly based on LoRaWan communication protocol -Long Range Wide-area network [START_REF] Augustin | A Study of LoRa: Long Range & Low Power Networks for the Internet of Things[END_REF]. LoRa is a technology commonly used in IoT projects and wireless sensor networks deployed in smart buildings and smart cities contexts [START_REF] Centenaro | Long-range communications in unlicensed bands: the rising stars in the IoT and smart city scenarios[END_REF][START_REF] Pasolini | Smart City Pilot Projects Using LoRa and IEEE802.15.4[END_REF]. It is relatively easy to implement, it provides information on the sensor status and it allows long-range data transmission even in areas with difficult access. LoRa technology is also cost-effective in terms of energy: it relies on radio waves with low communication rate and then low energy consumption. Several implementation strategies have been selected for the two presented instrumentation phases. The first phase is using an operated LoRa network with two gateways installed onsite. Only the electricity consumption-dedicated sensors use a GPRS network because of the limitations of operated LoRa network in terms of bandwidth usage (Electronic Communications Committee, 2019) and the selected acquisition time-step. The second phase is processed differently and separated into three subphases. As for shared areas, energy monitoring is entirely managedmeaning provided, installed and operatedby a contractor. Other sensors are provided and configured by a different service company and installed onsite by the research team in charge of the project. Finally, a ten-sensor sample (those combining measurement of indoor temperature, humidity, luminosity, presence and CO2 level for apartments) is entirely set up and installed by the research team. The LoRa network used is now a private network to bypass bandwidth usage constraints related to data acquisition time-step.

For all sensors, collected data are retrieved on a unique FTP server. The final format provides collected raw data with one csv file for each day and for each sensor. Information include the sensor identification and location, the type of measurements, the timestamp, the measured values and the units. Only data from the weather station are treated on a separated dedicated platform.

Instrumentation management process

Instrumentation overall management has a crucial impact on the success of the instrumentation and of the whole project. In the present study it can be divided into six different stages over an estimated timespan of one year and four months (started in October 2018 and expected to end in January 2020). First is the accurate definition of the instrumentation specifications to meet the needs of the project, as detailed in Section 3.1.1. In parallel, a review of service providers offering adapted solutions is performed and apartments are recruited to participate to the instrumentation study. Once specifications are organized in a clear framework, they are submitted to identified contractors. Several rounds of discussions allow modifications on the specifications to adapt to the reality of the market and for service providers to refine their offer to meet the needs of the project to the best of their capabilities. Every round dismisses several service providers to select the most relevant ones. In the present case a total number of thirty-three service providers have been contacted for a short-list of ten and two final selected contractors. Once a contract is signed, sensors are ordered, delivered and installed under the supervision of the research team. Finally, when the sensor network is functional, data quality is checked. It ensures that all sensors are properly measuring and transmitting data, that there are no missing information or other issues and that the proper data format is displayed for future applications.

IDENTIFTICATION OF CRITICAL POINTS FOR SENSOR NETWORK IMPLEMENTATION

The planning and deployment of the proposed instrumentation solution has highlighted several critical aspects in sensor network implementation. These critical points arose from various issues encountered during the instrumentation process. These can be grouped into four categories with i) onsite installation conditions and environment, ii) characteristics and purpose of instrumentation, iii) service provider and iv) project tracking and management.

Onsite installation conditions and environment

Characteristics of the experimentation site have a significant impact on the feasibility of a monitoring project. As a first step, it is crucial to precisely identify the equipment and installations to be monitored. Equipment conditions are also important, as for security reasons some may not be monitored. Indeed, over the selected ten-apartment sample, seven electrical switchboards could not be equipped because of their obsolescence and have to be replaced for the experimentation. Sensor connectivity must also be considered since metal stairs and doors disrupt radio waves and then data transmission. Finally, the installation environment should be documented. For instance, several sensors do not use batteries but need a main power supplythermal energy meters for instance. In the studied buildings, electrical installations were not adapted or even not existing where they were needed. Thus, additional costly actions were necessary to prepare the installation site.

The instrumentation solution described is also specific because all buildings remain occupied during the sensor network deployment and the whole experimentation. Then, the sensor network must as non-intrusive as possible. However, non-intrusive sensors imply higher costs because of specific technologies. Also, as the project mostly relies on collected data from apartments and occupants' behavior, it is necessary to recruit participants. Then, recruitment is a crucial step for the success of the research project, but is particularly time-consuming, requiring several rounds of presentations and visits (general presentation, door-to-door visits, phone calls and individual meetings). It also needs a wellprepared and transparent communication on the project. Project goals must be clearly stated, project actors must be identified, and inhabitants must find clear benefits in their participation. Finally, as most collected data are personal data, a specific attention should be given to related regulations and mandatory administrative actions (French Ministry of Economy, 2019).

Characteristics and purpose of the instrumentation solution

The introduced sensor network serves for a research project with specific needs. Therefore, it differs from usual commercial monitoring studies because it aims to investigate situations and details that would usually not be considered. More specifically, there are a wide range of acquisition time-steps (from one minute to one hour) and a large variety of sensors and measurements as presented in Table 1. Consequently, such a complex instrumentation solution faces several challenges. Sensors are designed for standardized usage conditions depending on the environment of installation and usually with hourly acquisition time-step. However, specific implementation characteristics imply that the sensors must respect specific standards, such as for gas consumption metering (Zone-atex.fr, 2019). Moreover, having sub-hourly acquisition time-steps is reducing the expected battery lifetime. This needs to be considered while selecting sensor technologies as it is not always possible to change the battery of sensors (due to manufacturing standards). Also, sensor technologies and measurement characteristics (especially the acquisition time-step) are defining the communication protocol selected for the sensor network. Indeed, several IoT communication protocols are available on the market such as operated and private LoRa networks, GPRS, Sigfox [START_REF] Sigfox | Sigfox -The Global Communications Service Provider for the Internet of Things (IoT)[END_REF] or Modbus (The Modbus Organization, 2019). However, they all have different characteristics, advantages and constraints. For instance, operated LoRa networks restrict bandwidth usage. Then having a one-minute time-step on large amounts of sensors is hardly possible. Private LoRa networks offer a solution but are more complicated to implement. Other solutions such as GPRS also raise different issues related to wireless monitoring technologies and electro-sensitivity.

Service providers and contractors

Through this study, service providers have been hired to provide an instrumentation solution adapted to the goals of the research project. On the French IoT market, there are many different contractors. However, they do not all provide the same delivery. Most commercial proposals focus on sensor provision but do not include set up and installation. Therefore, such contractors must partner with other companies to match the needs of a project. This often leads to many communication issues and delays. Furthermore, when a contract is established, all the terms must be carefully checked to ensure a smooth project process. Some points must be investigated and especially i) responsibilities and guarantees about the sensors/network and about the potential provision and installation delays, ii) maintenance details and conditions when included, and iii) what is done by the contractor with collected data during and after the contract validity.

Regarding technical aspects, it is necessary to ensure the service quality and expertise of contractors. Indeed, there is a significant difference between common "plug and play" sensorssuch as for temperature or humidity sensorsand energy metering. The latter requires very specific knowledge on the technologies, installation procedures and data acquisition checking. Moreover, many contractors do not have such equipment and need to partner with other manufacturers. Contractors with a lack of expertise should be avoided to prevent many future issues such as with sensor calibration or equipment failures.

Finally, the budget management requires a detailed investigation. Indeed, there can be several unexpected expenditure items which function is not always explained by contractors and that can significantly increase the total instrumentation budget. This include for instance accessories, connectivity subscriptions, details of all-inclusive maintenance contracts, installation and setup, or site visits. From the ten complete commercial proposals received for the present project, the total budget could be divided into 38% for sensors provision, 20% for installation, 20% for set up and data treatment software/platform, 9% for communication system, 8% for maintenance and 5% for project supervision.

Project management

The overall project management, comprising supervision on the three previous subsections, is the key to a smooth sensor network deployment and optimal valorisation. Regarding the instrumentation, a detailed and precise tracking is mandatory to identify every sensor with sensor type, measurements, communication protocol, installation date and location. This ensure that any potential issue will be solved with the minimum amount of time.

Adapted and controlled communication is essential within the research team to prevent any loss of information and miscommunication. It also must be ensured with other actors and particularly with building occupants. Indeed, it is recommended to avoid any over-soliciting with inhabitants for obvious privacy reasons. Finally, as the present research project is a multi-disciplinary study combining several research teams, an optimal coordination is needed. Objectives and tasks should be clearly defined for each actor. People in charge also must be designated for optimal communication and project tracking.

PRELIMINARY DATA ANALYSIS FROM THE FIRST INSTRUMENTATION PHASE

The first instrumentation phase focusing on building common areas is fully operational. Thus, a statistical data analysis is performed on an observation window from 2019/02/19 to 2019/10/06 to highlight issues in collected data. Twenty sensors are considered including data for temperature & humidity (9 sensors hourly time-step), passage counting (3 sensorshourly time-step), thermal energy (3 meters -5minute time-step) and electric power demand monitoring (5 sensors -1-minute time-step).

The main highlighted issue relates to missing datapoints. Over the given observation period, 92.7% of the expected datapoints are collected. Figure 2 compares the evolution of expected measurements (blue curve) and of the effective collection results (orange curve) with the variation of the percentage of acquired data (green curve). The major gap is due to a 17-day-long sensor malfunction in May 2019 for the electrical switchboard monitoring. Electricity demand data collection is therefore the category with the least collected datapoints (on Figure 3: 92.0% of the optimal target), followed by thermal energy monitoring (94% of data collected). Indoor environment and passage counting account for more than 99% of collected data. However, large amounts of missing energy measurements should also be transposed to time-scale analysis. Indeed, electric sensors provide one-minute time-step information. Hence, over a 230-day observation period, it would be equivalent a loss of less than 19 days of data and in the present case essentially concentrated on a specific period for one specific sensor. Other observed outliers are abnormal and additional measurements. Abnormal values are only found for energy demand monitoring, with overly high measurements or zero-values. The former represents 0.06% of total datapoints while the latter accounts for 6.8% of the amount of collected data and is almost exclusively related to electrical switchboard monitoring (99.9% of abnormal measures). Also, such measurements should be further analyzed from an energy-behavior point of view. Indeed, unexpected zero power demand can be related to data loss but also to potential power cuts that are part of the building energy behavior.

CONCLUSIONS AND FUTURE WORK

This paper presents the planning, deployment and supervision of a sensor network for existing residential buildings monitoring. The proposed solution is a multi-scale sensor network covering thermal and electrical energy consumption, indoor environment and comfort, inhabitants' behaviour and weather conditions, at various timescales from oneminute to hourly. The instrumentation solution has been entirely planned and divided into two implementation phases. The first phase focuses on the monitoring of building shared areas and is entirely operational. The second phase considers a similar approach on a ten-apartment sample and will be deployed starting from November 2019. Details of both phases are presented with a description of sensor characteristics, communication networks and overall project management.

A feedback on the sensor network implementation from the first phase is proposed. It highlights several critical points to consider for similar future applications. These critical aspects are grouped in four categories with onsite installation conditions and environment, characteristics and purpose of the instrumentation solution, service provider and contractors and project management. A preliminary statistical analysis of collected data is also provided.

It highlights the main encountered issues in data collection.

Data analysis should then be extended to measurements from the operation of the second instrumentation phase. Moreover, in order to ensure long-term measurement accuracy and to prevent future avoidable data loss and highlighted data collection issues, a long-term calibration study must be conducted. Finally, data analysis should be further conducted from an energy point-of-view. It would aim to highlight the specificities of building-and apartment-scale energy behaviours and investigate potential issues in building energy management.

Figure 1 :

 1 Figure 1: Installation example a thermal energy meter for heating energy demand monitoring

Figure 2 :

 2 Figure 2: Evolution of collected datapoints (orange) compared to expected collected datapoints (blue) from 2019/02/19 to 2019/10/06

Figure 3 :

 3 Figure 3: Comparison of collected datapoints (orange) compared to expected collected datapoints (blue) for the different monitoring categories

Table 1 :

 1 Characteristics summary of the deployed sensors

	Sensor	Number at building scale (per building)	Number per apartment	Total number	Acquisition time-step	Communication protocol
	Indoor temperature & humidity	3	/	9	Hourly	Operated LoRa
	Presence	1	/	3	Hourly	Operated LoRa
	Combined indoor temperature,
	humidity, luminosity, presence	/	1	10	Hourly	Private LoRa
	& CO2 level
	Exterior walls surface temperatures	/	2-5	32	Hourly	Private LoRa
	Window opening detection	/	3-5	38		Private LoRa
	Gas consumption	/	0-1	4	One-minute	Private LoRa
	Electricity demand -main electric meter	2-3	1	17	One-minute	GPRS
	Electricity demand -switchboard	0-1	1	11	One-minute	GPRS
	Electricity demand -smartplugs	/	5-9	67	One-minute	Private LoRa
	Heating energy demand -
	thermal energy meter & pulse	1 + 1	/	3 + 3	Five-minute	Operated LoRa
	sensor
	Heating energy demand -radiators	/	3-5	36	Hourly	Private LoRa
	Domestic hot water energy
	demand -thermal energy meter	1 + 1	/	3 + 3	One-minute	Private LoRa
	& pulse sensor
	Domestic hot water energy demand -apartments	/	2	20	One-minute	Private LoRa