©valérie Vandenabeele

What to say about the perception of nature in China today? The Chinese language proposes to consider what we call "nature" as "[what is] so from itself", ziran 自然. This view of nature as being what occurs spontaneously refers to the phenomena which happen independently of the human will and whose mysterious origin may arouse our questioning and our wonder, such as the germination of a seed or the growth of an individual. It refers, on the one hand, to the idea of a principle which imposes itself upon human beings and on the other hand, to the dominant trends of Chinese thought which advocate the permanent balancing of humans to the world's spontaneous movement. Simultaneously, China is known for the long history during which it has intensively transformed and exploited nature, on the initiative of its leaders, since its legendary emperor Yu the Great who is associated to the building of canals around 2200 B.C.

On the one hand, the setting of the first National Park of the country in 2006 shows that the management of nature is dominated by the political view, without concern for this of the classical thinkers. On another hand, the physicians' horizon of refining in order to adjust oneself to the rhythm of nature seems no longer topical further to the redefinition of Chinese medicine under Mao's government. Globalization currently fosters the spread of the idea of interdependence of everything at the basis of ecology as well as the multiplication of meetings between China and the West. And if these phenomena had an influence on the future of China's contribution about nature?

A place to be marked by the culture of the political order China's first National Park (Zhongguo di yi ge guojia gongyuan 中国第一个国家公园1 ), which opened in Northwestern Yunnan on the 1 st of August 2006, provides a good example to grasp a first facet of the current notion of « nature » in China.

Location map of Pudacuo National Park base map: Daniel Dalet, © histgeo.ac-aix-marseille.fr, CAD: Valérie Vandenabeele This achievement results from the initiative of a US NGO and above all from the will of the political authorities of the Diqing prefecture and the Shangrila county. The objective of developing mass tourism led to the choice of an area situated at around one-hour drive from the prefectoral capital and its airport, without concern for the pollution caused in this area by previous tourist activities. Nature has been laid out to allow visitors to discover high altitude lakes surrounded by mountains, which correspond to the ideal Chinese landscape combining mountain and water, the "shanshui " 山水 .

Shudu lake or the « shanshui » ideal landscape, 10/2008, ©Valérie Vandenabeele

Travelers are invited to discover the local setting via a winding road of about sixty kilometres, which crosses meadows and forests. Every element of the layout fosters the impression of having a low impact on the environment: supposedly "ecological" buses and toilet, stopping platforms and wooden signs, footbridges which seem to integrate respectively among trees.

Simultaneously, the visit gives the opportunity to learn that the preserved state of the park's spaces results from the culture of the local Tibetans. These are not necessarily seen by travelers and are portrayed as spontaneously respectful of the natural environment as a result of their practice of Tibetan Buddhism and their agropastoral lifestyle. This statement which values Tibetans and acknowledge their ability to manage the natural environment is recent and is in line with the tourist discourse which identifies "minority nationalities", that is non-Han Chinese, to the concern for the natural environment, discourse which bases Yunnan's economic development through tourism since the end of the 1990s. It also echoes the "green Tibetans"' imagery, which ascribes the Tibetans the faculty to live in harmony with nature and to have an innate knowledge of its mechanisms, imagery which was developed at the initiative of the WWF and the Tibetan Government in Exile since 1985.

Hence the incredible success of the park, where more than two million persons had gone three years and a half after its opening, for a fee of 190 yuan (about 19€ at that time), allowing the prefectoral government to obtain more than 350 million yuan of income.

But for the local political decision-makers, this presentation is only a tourist argument and the relationship to nature of the Tibetan villagers who live in the park or in its surroundings has no interest. Only their view counts: that of a nature to exploit and of a wild space on which to impose their seal and whose "barbaric" populations are to be civilized, which concurs with that of former emperors. On the one hand, they seek to take advantage of the Pudacuo area through the "National Park" certification label. On the other hand, they have shaped the local space and they aim at sinicizing local Tibetans in giving them allowances which ensure their better integration to the consumer society and contemporary China [START_REF] Valérie | Les nouveaux horizons. Politique sino-tibétaine et écologie au Yunnan[END_REF].

Nature as horizon for the man of culture

Nature has also been instituted as a life principle with which it is necessary to match by the classical thinkers such as the Taoist Zhuangzi (4 th century BC) and Laozi (6 th to 5 th century BC), the followers of the analogical thought and the Buddhists. For them, we have to melt into what occurs spontaneously, to live in a state considered as "non-action or rather action-which espouses nature" (wuwei 无 为 ) (Cheng 2002 : 133). Among other things, this horizon consists in learning to manage one's emotions and in accepting what happens, and it would enable to experience a long and nice life as well as to accede to the aptitude of knowing which gives little importance to the intellect.

This ideal lies at the heart of "the martial, gymnastic, respiratory, visualising and mental concentration techniques, trance or hypnosis techniques" developed in Taoism, Buddhism, Confucianism and Chan meditation (zen in Japan), which were gathered within qigong (气功), literally "the work on qi", that is "on breath, on energy", at the beginning of the twentieth century (Despeux 1997 : 268).

The aim of these techniques shows how the human body and health are considered in China. By example, it comes from the view of the world as a set of elements animated by this same thing called qi 气 , from which it follows that the body is permeable to its surroundings. In addition, the recommendation not to follow the intellect refers to the idea that the individual's guide lies in his heart/mind (xin 心) rather than in his brain. And again: the recommendation to manage one's emotions refers to the idea that the disorder of the mind can induce a disorder of the body. These techniques are at the basis of the traditional training of doctors because they are considered to enable the development of the skill to perceive disorders and to regulate them. The more a therapist engages in the work on his qi, the more he would be able to disregard his emotions, to be fully aware of his feelings therefore to be sensitive to the imbalances that affect the bodies of his patients. In other words, medical expertise is seen as the result of the physical refining of the doctor. This is shown through the therapeutic massage tuina 推拿 and acupuncture, in which the therapist must mobilise his body to supply the patient with qi, giving his own qi or being the channel of the qi of the cosmos.

However, this reasoning does not lie in the activity of most of practitioners today. The desire to make Chinese medicine credible to Westerners led to its "modernisation", under the aegis of the intellectuals of the beginning of the twentieth century and Mao. References to notions that could be seen as "superstitions" and which were supposed to have no role in the therapeutic process such as qi now have little importance in the Chinese medicine university curriculum. The practice of Chinese medicine by persons who do qigong has nonetheless not totally disappeared. But what about the way they perceive body and health today, in the context of marginalisation of their analysis framework and of the predominance of biomedicine? How do they live their sensory refining while Chinese society glorifies cerebral formulation? Do their practices lead them to experience the Chinese classical representations of body and health? Do they consider them as knowledge? As beliefs?

This situation brings back to the opposition between the invitation to conform to nature expressed by classical thinkers and the will of political leaders to subjugate it. Keeping this tension in mind, we can wonder whether Chinese still explain illness as the result of the imbalance between the human body and the world's spontaneous movement; to what extent they consider that the solving of health problems requires the resort to biomedical invasive techniques; or what became the perception of nature as an horizon of human development.

Nature and culture in globalized China

The interrelation between nature and culture takes several forms in China and is structured around a strong tension between politicians and thinkers. Today, it tends to spread all over the world via the increasing importance of Chinese immigration and the attraction of more and more Westerners for this cultural melting pot. On the one hand, the exploitation of natural resources and the sensitization of "wild lands", that is "non-Han", are now taking place very largely, from Laos to Africa and South America. On the other hand, the omnipresence of the idea of interdependence between everything at the basis of ecology, the distrust for biomedicine and the rejection of the perception of the world through an approach exclusively intellectual in the West make it a fertile ground for Chinese classical thought.

Valérie

  Vandenabeele, « Nature and culture in China », in Jean-François Sabouret (éd.), version anglaise de la Lettre du GIS-Réseau Asie et Pacifique, 04/2018, http://www.gis-reseau-asie.org/monthlyarticles/nature-et-culture-en-chine-vandenabeele-valerie.

The phrase "National Park" has been misused to refer to Chinese "national-level nature reserves" ( guojia ji ziran baohu qu 国家级自然保护区) in Western literature.


Lester Kwiatkowski
email: lester.kwiatkowski@lsce.ipsl.fr

Laurent Bopp

Olivier Aumont

Philippe Ciais

Peter M Cox

Charlotte Laufkötter

Yue Li

Roland Séférian

Roland Seferian

Emergent constraints on projections of declining primary production in the tropical oceans

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

still project a wide range of global ocean primary production changes within the 21 st century [START_REF] Bopp | Multiple stressors of ocean ecosystems in the 21st century: projections with CMIP5 models[END_REF] . Under the business-as-usual Representative Concentration Pathway 8.5 (RCP8.5) scenario [START_REF] Riahi | RCP 8.5-A scenario of comparatively high greenhouse gas emissions[END_REF] , models project global NPP declines of 0-20% in the 2090s relative to 1990s [START_REF] Bopp | Multiple stressors of ocean ecosystems in the 21st century: projections with CMIP5 models[END_REF] (Fig. S1). Projected global declines are driven by reductions in NPP in the equatorial and sub tropical biomes [START_REF] Cabré | Consistent global responses of marine ecosystems to future climate change across the IPCC AR5 earth system models[END_REF] due to stratification-driven reductions in nutrient availability as well as increases in grazing and other phytoplankton loss processes [START_REF] Laufkötter | Drivers and uncertainties of future global marine primary production in marine ecosystem models[END_REF] . These reductions are slightly compensated for by increases in NPP at high latitudes [START_REF] Laufkötter | Drivers and uncertainties of future global marine primary production in marine ecosystem models[END_REF][START_REF] Cabré | Consistent global responses of marine ecosystems to future climate change across the IPCC AR5 earth system models[END_REF] .

The current uncertainty associated with future NPP changes is larger across ESM ensembles than across different scenarios of climate change [START_REF] Bopp | Multiple stressors of ocean ecosystems in the 21st century: projections with CMIP5 models[END_REF][START_REF] Cabré | Consistent global responses of marine ecosystems to future climate change across the IPCC AR5 earth system models[END_REF][START_REF] Frölicher | Sources of uncertainties in 21st century projections of potential ocean ecosystem stressors[END_REF] . Constraining estimates of the climate sensitivity of tropical ocean primary production is one of the major challenges in understanding how the ocean carbon cycle and marine food web will respond to future climate change [START_REF] Laufkötter | Drivers and uncertainties of future global marine primary production in marine ecosystem models[END_REF] .

The use of emergent inter-model relationships in conjunction with observational constraints is one of the recent advances in reducing the uncertainty of climate projections [START_REF] Hall | Using the current seasonal cycle to constrain snow albedo feedback in future climate change[END_REF][START_REF] Boé | September sea-ice cover in the Arctic Ocean projected to vanish by 2100[END_REF][START_REF] Cox | Sensitivity of tropical carbon to climate change constrained by carbon dioxide variability[END_REF][START_REF] Wenzel | Projected land photosynthesis constrained by changes in the seasonal cycle of atmospheric CO2[END_REF][START_REF] Allen | Constraints on future changes in climate and the hydrologic cycle[END_REF] . Emergent inter-model relationships relate the long-timescale climate sensitivity of a given variable to the sensitivity to shorttimescale variability or trend of the same or a related variable, across a multi-model ensemble. Observations of the short timescale sensitivity can then be applied to the emergent relationship to infer a constrained long-timescale sensitivity of the variable of interest. Such techniques have been used to reduce uncertainty in projections of Arctic summer sea ice [START_REF] Hall | Using the current seasonal cycle to constrain snow albedo feedback in future climate change[END_REF][START_REF] Boé | September sea-ice cover in the Arctic Ocean projected to vanish by 2100[END_REF] and terrestrial tropical carbon fluxes [START_REF] Cox | Sensitivity of tropical carbon to climate change constrained by carbon dioxide variability[END_REF][START_REF] Wenzel | Projected land photosynthesis constrained by changes in the seasonal cycle of atmospheric CO2[END_REF] .

Utilising the Coupled Model Intercomparison Project Phase 5 (CMIP5) ESM ensemble (Table S1), we identify an emergent relationship between the interannual sensitivity of tropical (30°N-30°S) marine NPP to ENSO driven SST anomalies in the Niño 3.4 equatorial zone region (5°N-5°S, 120°W-170°W) and the long-term sensitivity of tropical marine NPP to climate change driven SST anomalies in the Niño 3.4 region. In defining tropical NPP sensitivity relative to Niño 3.4 region SST anomalies, intrinsic ENSO climate variability, which is highly variable across the ESM ensemble, is accounted for.

The existence of such an emergent relationship implies that, for a given model, the response of tropical NPP to long-term climate change is governed by similar processes to those that determine the interannual sensitivity of NPP to ENSO variability. It does not require that all models have the same dominant mechanisms. Indeed, for certain models the dominant mechanism controlling interannual and long-term NPP sensitivity is nutrient limitation while in other models it appears to be zooplankton grazing and other phytoplankton loss terms [START_REF] Laufkötter | Drivers and uncertainties of future global marine primary production in marine ecosystem models[END_REF] (Fig. S2).

The sensitivity of tropical NPP to ENSO variability was diagnosed for each model from the last 200 years of pre-industrial control simulations as the linear regression coefficient between Niño 3.4 region SST anomalies and tropical NPP anomalies. All the models exhibit a negative relationship (P <0.02) between SST anomalies in the ENSO driven Niño 3.4 region and anomalies in tropical NPP (Fig. 2a,S3). NPP declines are typically driven by reductions in NPP in the central and eastern tropical Pacific and in certain models offset by increases in NPP in the western Pacific and eastern Indian Ocean (Fig. S4).

The long-term climate impact on NPP was diagnosed from RCP8.5 simulations as the decline in tropical NPP relative to 1990-2000 values, per degree of Niño 3.4 region SST warming. This was calculated for each model as the linear regression coefficient between NPP and SST anomalies with all models exhibiting inverse relationships (P <0.001; Fig. 2b,S5).

Across the multi-model ensemble there is a strong positive correlation (r =0.91, P <0.001) between the interannual sensitivity of tropical NPP to ENSO driven SST variability and the long-term sensitivity of tropical NPP to climate change in the 21 st century (Fig. 3). Models with higher interannual NPP sensitivity to SST anomalies in pre-industrial simulations consistently project greater declines in tropical NPP per degree warming in the 21 st century (Fig. 3).

Marine NPP, unlike chlorophyll concentrations, cannot be directly measured from space. Consequently multiple products of NPP that use satellite chlorophyll and incident light data, in combination with descriptions of phytoplankton physiology have been developed [START_REF] Carr | A comparison of global estimates of marine primary production from ocean color[END_REF] . Given that these NPP products can have large discrepancies [START_REF] Carr | A comparison of global estimates of marine primary production from ocean color[END_REF] , we derive observational constraints from four algorithms over the Seaviewing Wide Field-of-View Sensor (SeaWIFS) satellite record (Fig. 2a,S6): the Vertically Generalised Production Model (VGPM) [START_REF] Behrenfeld | Photosynthetic rates derived from satellite-based chlorophyll concentration[END_REF] , the Carbon-based Production Model (CbPM) [START_REF] Behrenfeld | Carbon-based ocean productivity and phytoplankton physiology from space[END_REF] [START_REF] Carr | Estimation of potential productivity in Eastern Boundary Currents using remote sensing[END_REF] . Observational constraints on the interannual sensitivity of tropical NPP to Niño 3.4 region SST anomalies were calculated as the linear regression coefficient between each NPP algorithm and the contemporaneous Hadley Centre Sea Ice and Sea Surface Temperature data set 31 (HadISST1). The resulting constraints are -3.2±1.3, -2.8±0.9, -1.5±0.4 and -2.1±0.6 % K -1 (standard errors) for the VGPM, CbPM, Marra and Carr algorithms over the period 1998-2008, respectively.

Applying the observational constraints to the multi-model emergent relationship leads us to infer estimates of the long-term sensitivity of tropical primary production to future Niño 3.4 region SST warming of between -3.4±1.3 % K -1 (VGPM) and -2.4 ±1.1 % K -1 (Marra). There is therefore close agreement between the observational constraints, all of which substantially reduce the uncertainty relative to the unconstrained ensemble PDF (-4.0±2.2 % K -1 ; Fig. 3b). The application of observational constraints greatly reduces the probability that declines in long-term NPP will exceed 6 % K -1 . In the unconstrained ensemble this has a probability of 18 %. This is reduced to <1.8 % for all observational constraints. Although no individual model predicts a positive long-term climate impact on tropical NPP (>0 % K -1 ), this has an unconstrained probability of 3.5 % and has been projected in other studies [START_REF] Laufkötter | Drivers and uncertainties of future global marine primary production in marine ecosystem models[END_REF][START_REF] Taucher | Can we predict the direction of marine primary production change under global warming?[END_REF] . This probability is reduced to <1.5 % when all four constraints are applied. Given the multi-model mean RCP8.5 Niño 3.4 region SST anomaly is 3.9±1.3 K in 2100 relative to the 1990s, our emergent constraints imply a 21 st century tropical NPP decline of between 13.0±6.5 % (VGPM constraint) and 9.3±5.1 % (Marra constraint) under this business-as-usual scenario.

As the CMIP5 projections of global NPP decline are predominantly driven by changes in the tropical oceans [START_REF] Laufkötter | Drivers and uncertainties of future global marine primary production in marine ecosystem models[END_REF][START_REF] Bopp | Multiple stressors of ocean ecosystems in the 21st century: projections with CMIP5 models[END_REF][START_REF] Cabré | Consistent global responses of marine ecosystems to future climate change across the IPCC AR5 earth system models[END_REF] , constraints on the sensitivity of tropical NPP can also be used to reduce the uncertainty associated with the long-term sensitivity of global NPP (Fig. S8). The unconstrained global NPP sensitivity is -2.3±1.2 % per kelvin increase in Niño 3.4 region SST anomaly while the constrained estimates are between -1.9±0.7 % K -1 and -1.4±0.6 % K -1 (Fig. S8). Given the multi-model mean Niño 3.4 region SST anomaly of 3.9±1.3 K, this implies a 21 st century global NPP decline of between 7.0±3.4 % (VGPM constraint) and 5.4±3.0 % (Marra constraint) under the RCP8.5 scenario.

Although the emergent constraints on tropical NPP are robust for RCP8.5, alternative scenario processes could influence the slope of the multi-model emergent relationship and therefore the constraints. In particular, the extent of future natural and anthropogenic nutrient deposition and transient enhancement of deep ocean mixing under certain climate mitigation scenarios [START_REF] John | A more productive, but different, ocean after mitigation[END_REF] .

Our analysis highlights the need to reconcile the apparent differences between the mechanisms driving NPP sensitivities in different ESMs [START_REF] Laufkötter | Drivers and uncertainties of future global marine primary production in marine ecosystem models[END_REF] (Fig. S2). This will require future multi-model intercomparison projects to provide phytoplankton growth rates and loss terms in addition to NPP so that the relative contribution of bottom-up and top-down limitation can be assessed throughout the photic zone and ensured consistent with observations. Future refinements of emergent constraints on NPP projections will require more expansive ESM ensembles as well as longer satellite chlorophyll records that encompass multiple large-scale ENSO events. There is also a need to consolidate the diverse array of NPP algorithms and ensure that they provide accurate descriptions of photoacclimation so that NPP estimates are reliable [START_REF] Behrenfeld | Revaluating ocean warming impacts on global phytoplankton[END_REF] .

Emergent constraints on tropical marine primary production projections substantially increase our confidence that rising SSTs will result in a long-term decrease in tropical NPP throughout the 21 st century while simultaneously reducing the probability of the most extreme projections of tropical NPP decline. Given that marine primary production is the ultimate control on the energy available to the marine food web [START_REF] Pauly | Primary production required to sustain global fisheries[END_REF][START_REF] Friedland | Pathways between Primary Production and Fisheries Yields of Large Marine Ecosystems[END_REF] , tropical NPP declines may have cascading and potentially amplified impacts on higher trophic levels, and on the goods and services they provide [START_REF] Barber | Ocean variability in relation to living resources during the 1982-83 El Niño[END_REF] . More accurate projections of declining tropical NPP may also prove useful for a better ecosystem-based management of fisheries across the tropical oceans. T r opi c a l pr i ma r y pr oduc t i on a noma l y ( %)

Obs (Carr) Obs (Marra)

Methods

Earth System Models

Depth integrated marine primary production model output was taken from the Coupled Model Intercomparison Project Phase 5 (CMIP5) ensemble of 13 ESMs that ran coupled ocean biogeochemistry schemes (Table S1). All models reached close to equilibrium NPP values prior to the last 200 years of pre-industrial control simulations. The sensitivity of multi-model emergent relationships to the future climate scenario and the NPP depth integral is shown in the supplementary information.

Observational constraints

To assess the sensitivity of results to the applied observational constraint, four net primary production estimates based on different remote sensing algorithms were used, the Vertically Generalised Production Model (VGPM) [START_REF] Behrenfeld | Photosynthetic rates derived from satellite-based chlorophyll concentration[END_REF] , the Carbon-based Production Model (CbPM) [START_REF] Behrenfeld | Carbon-based ocean productivity and phytoplankton physiology from space[END_REF] [START_REF] Carr | Estimation of potential productivity in Eastern Boundary Currents using remote sensing[END_REF] . The VGPM, Carr and Marra algorithms all contain chlorophyll-specific carbon fixation efficiency terms that are a function of SST whereas the CbPM derives phytoplankton growth rates directly from satellite based carbon-to-chlorophyll ratios without using SST to characterise phytoplankton physiology.

The observed sensitivity of tropical primary production to SST anomalies in the Niño 3.4 region was diagnosed for the different NPP estimates using the contemporaneous HadISST1 31 SST record based on Advanced Very High Resolution Radiometer (AVHRR) measurements over the Sea-viewing Wide Field-of-View Sensor (SeaWIFS) satellite record (1998-2008; Fig. 2a,S6). The SeaWIFS record was used in order to encompass a major El Niño-La Niña transition during which there was large primary production variability [START_REF] Behrenfeld | Biospheric Primary Production During an ENSO Transition[END_REF] . A merged product of different satellite records was avoided to prevent any potential biases affecting observational constraints. The timescale of the observational records is such that they are dominated by ENSO variability and therefore unlike other studies (e.g. [START_REF] Cox | Sensitivity of tropical carbon to climate change constrained by carbon dioxide variability[END_REF] ), there is no need to remove a long-term climate signal by detrending.

PDFs of long-term primary production sensitivity

Probability density functions (PDFs) of the long-term SST sensitivity of tropical primary production were calculated for the unconstrained (prior) CMIP5 ensemble and the VGPM, CbPM, Marra and Carr emergent constraints. The prior PDF was derived assuming all models were equally likely and sampled from a Gaussian distribution. The constrained PDFs were calculated following previously established methodologies [START_REF] Cox | Sensitivity of tropical carbon to climate change constrained by carbon dioxide variability[END_REF] . The PDFs of the VGPM, CbPM, Marra and Carr observational constraints are defined as:

𝑃(𝑥) = 1 2𝜋𝜎 ! ! 𝑒𝑥𝑝 (𝑥 -𝑥) ! 2𝜎 ! !
where 𝑥 is the least-squares linear regression coefficient of NPP observations regressed against the Niño 3.4 region HadISST record and 𝜎 ! is the corresponding standard error (Fig. S6).

The 'prediction error' of the emergent multi-model linear regression (𝜎 ! (𝑥)) defines contours of equal probability density around the multi-model linear regression, which represent the probability density of y given x:

𝑃(𝑦|𝑥) = 1 2𝜋𝜎 ! ! 𝑒𝑥𝑝 (𝑦 -𝑓 𝑥 ) ! 2𝜎 ! !
where 𝜎 ! = 𝜎 ! (𝑥).

Given the PDFs 𝑃 𝑦|𝑥 and 𝑃 𝑥 , the observationally constrained PDF for y is:

𝑃(𝑦) 𝑃 𝑦|𝑥 𝑃 𝑥 𝑑𝑥 ! !!
Additional potential prior PDFs that weigh models based on their respective model family, ocean biogeochemistry scheme, or based on their relationship to observational PDFs are given in the supplementary material. All observationally constrained PDFs substantially reduce the uncertainty in projections of the long-term sensitivity of NPP relative to all potential prior PDFs (Fig. S7). As the longterm global primary production declines across the CMIP5 ensemble are driven by declines in the tropics [START_REF] Laufkötter | Drivers and uncertainties of future global marine primary production in marine ecosystem models[END_REF][START_REF] Cabré | Consistent global responses of marine ecosystems to future climate change across the IPCC AR5 earth system models[END_REF] , the same approach can be utilised to constrain long-term projections of global NPP decline (Fig. S8).

FiguresFigure 1 .

 1 Figures

Figure 2 .

 2 Figure 2. Primary production ENSO sensitivity and projected climate impact. a, The annual mean anomaly in tropical primary production against the annual mean Niño 3.4 region SST anomaly for CMIP5 pre-industrial control simulations (coloured lines) and observations (dashed black lines). b, The annual mean anomaly in tropical primary production relative to 1990s mean values against the annual mean Niño 3.4 region SST anomaly for CMIP5 RCP8.5 simulations. All linear regressions are significant at the P <0.05 level.

  p i c a l p r i ma r y p r o d u c t i o n a n o ma l y ( %)

Figure 3 .

 3 Figure3. Emergent constraints on the sensitivity of tropical marine primary production to climate change. a, The long-term sensitivity of tropical primary production to Niño 3.4 region SST anomalies against the interannual sensitivity of tropical primary production to Niño 3.4 region SST anomalies. The best-fit observational constraints derived from the different primary production products are shown as solid vertical lines with dashed lines indicating ±1 standard error. b, the probability density functions (PDFs) of the long-term SST sensitivity of tropical primary production. The black line shows the 'prior' PDF, assuming all models are equally likely and from a Gaussian distribution. The coloured lines show the four observationally constrained PDFs.

  , the Marra et al. 2003 model (Marra) 29 and the Carr et al. 2002 model(Carr)

  , the Marra et al. 2003 model (Marra) 29 and the Carr et al. 2002 model(Carr)

2000 2002 2004 2006 2008 Year

Acknowledgements

This study was funded by the ERC IMBALANCE-P synergy grant (ref 610028) and the H2020 CRESCENDO grant (ref 641816). We acknowledge the World Climate Research Programme's Working Group on Coupled Modelling, which is responsible for CMIP. For CMIP the US Department of Energy's Program for Climate Model Diagnosis and Intercomparison provided coordinating support and led the development of software infrastructure in partnership with the Global Organisation for Earth System Science Portals. To analyse the CMIP5 data, this study benefited from the IPSL Prodiguer-Ciclad facility which is supported by CNRS, UPMC, Labex L-IPSL which is funded by the ANR (ref ANR-10-LABX-0018) and by the European FP7 IS-ENES2 project (ref 312979).

Data availability

The data that support the findings of this paper are available from the author on request. All ESM model output is available via the Earth System Grid Federation (ESGF).

Author Contributions

L.K. and L.B. led the study. R.S. provided observational data. C.L. and P.M.C. provided analytical assistance. All co-authors contributed to the manuscript.

Author information

The authors declare no competing financial interests. Correspondence and requests for materials should be addressed to L.K.


Charles André
email: candre@sophia.inria.fr

Frédéric Mallet
email: fmallet@sophia.inria.fr

Robert De Simone

Modeling Time(s)

Keywords:

Time and timing features are an important aspect of modern electronic systems, often of embedded nature. We argue here that in early design phases, time is often of logical (rather than physical) nature, even possibly multiform. The compilation/synthesis of heterogeneous applications onto architecture platforms then largely amounts to adjusting the former logical time(s) demands onto the latter physical time abilities. Many distributed scheduling techniques pertain to this approach of "time refinement". We provide extensive Time and Allocation metamodels that open the possibility to cast this approach in a Model-Driven Engineering light. We give a UML representation of these concepts through two subprofiles, parts of the foundations of the forthcoming OMG UML Profile for Modeling and Analysis of Real-Time and Embedded systems (MARTE). Time modeling also allows for a precise description of time-related entities and their associated timed properties.

Introduction

Modeling of Time should be a central concern in Model-Driven Engineering for Real-Time Embedded systems. Nevertheless, (too?) many modeling frameworks consider Time annotations as to be considered in timing/schedulability/performance, and accordingly build uninterpreted stereotypes and label locations with insightful names only for the future analysis tool (and no meaning at all for the time augmented profile). Given that the default operational semantics of the UML is inherently untimed, and rightfully so since there is no Time information in the ground metamodel, one can reach the situation where the same model can be understood differently depending on whether it is considered from the UML causality model or the intended timed analysis viewpoint. Our primary goal here is to lay the foundation for a Time model which could be deeply embedded in UML as a profile allowing the subsequent clean and precise definition of a timed causality model enforcing timed operational semantics of events and actions.

Following some works on dedicated Models of Computation and Communication (MoCCs) for real-time embedded systems [START_REF] Lee | A framework for comparing models of computation[END_REF][START_REF] Buck | Ptolemy: A framework for simulating and prototyping heterogeneous systems[END_REF][START_REF] Jantsch | Modeling Embedded Systems and SoCs -Concurrency and Time in Models of Computation[END_REF], we view Time in a very broad sense. It can be physical, and considered as continuous or discretized, but it can also be logical, and related to user-defined clocks. For instance, durations could be counted in terms of numbers of execution steps, or clock cycles on a processor or even more abstract time bases, without a strong relation to the actual physical duration (which may not be known at design time, or fluctuate, or be a parameter that allows the same model to be instantiated under different contexts and speeds). With modern embedded designs where, for low-power reasons, the actual processor clock can be shut down and altered at times, such usage of logical time in the application design will certainly become customary. In our approach, time can even be multiform, allowing different time threads to progress in a non-uniform fashion.

This approach looks certainly non-standard, but is getting increasing interest from a number of directions. A mostly untimed concurrent application can be considered as comprising several unrelated (or loosely coupled) time threads (thereafter called "clocks", not to be confused with the physical measurement device which we will never consider). The process of allocating the various operations/functions/actions of such a concurrent model onto an embedded execution platform comprises aspects of spatial distribution and temporal scheduling. This is accomplished by resolving the mutual sets of timing constraints imposed by the designer of the time scales of the application, the target architecture, and the real-time requirements to be met. We call the approach one of Time refinement.

A number of existing transformation techniques can be cast in this framework. Nested loop scheduling and parallelization [START_REF] Darte | Scheduling and Automatic Parallelization[END_REF][START_REF] Feautrier | Compiling for massively parallel architectures: a perspective[END_REF] in high-performance computing, software pipe-lining, SoC synthesis phases from so-called transactional level (TLM) down to cycle-accurate RTL level, to mention a few. In all cases, the purpose is to progressively refine the temporal structure, which starts with a number of degrees of freedom, to attain a fully scheduled and precisely cycleallocated version, with predictable timing. In that sense our model allows, and it is in fact its primary aim, to describe formal clock relations in a simple mathematical way.

We provide a UML model for Time in its different guises, physical/logical, dense/discrete, single/multiple, and some useful basic operators and relations to combine timed events or clocks. From this set of primitives, we hope to build explicit representation of MoCCs, and to provide a Timed causality model to endow the timed models with a timed semantics, according to the one that would be considered by analysis tools. When the relation are simple enough (periodic or regular), the system of contraints imposed by these relations can be solved, and the schedule itself becomes an explicit modeling element, traceable to the designer. In other, more complex cases, the constraints embody a given scheduling policy, which can be analyzed with corresponding schedulability analysis techniques when applicable.

After describing some existing time and allocation models (Section ??), Section ?? introduces our contribution, the MARTE2 subprofiles for time and allocation. Section ?? briefly illustrates their use.

Existing time and allocation models

Time modeling

This subsection focuses on time models and time-related concepts in use in the UML and some of its profiles.

UML In UML [6] Time is seldom part of the behavioral modeling, which is essentially untimed (by default, events are handled in the same order as they arrive in event handlers). UML describes two kinds of behaviors [START_REF] Selic | On the semantic foundations of standard uml 2.0[END_REF]: the intra-object behavior-the behavior occurring within structural entities-and the inter-object behavior, which deals with how structural entities communicate with each other. The CommonBehaviors package defines the relationship between structure and behavior and the general properties of the behavior concept. A subpackage called SimpleTime adds metaclasses to represent time and duration, as well as actions to observe the passing of time. This is a very simple time model, not taking account of problems induced by distribution or by clock imperfections. In particular the UML causality model, which prescribes the dynamic evaluation mechanisms, does never refer to time (stamps). Instead, the UML specification document explicitly states that "It is assumed that applications for which such characteristics are relevant will use a more sophisticated model of time provided by an appropriate profile". Our contribution can be seen as providing the means for building such sophisticated time models.

SPT The UML Profile for Schedulability, Performance, and Time (SPT) [START_REF]OMG: UML Profile for Schedulability, Performance, and Time Specification[END_REF] aimed at filling the lacks of UML 1.4 in some key areas that are of particular concern to real-time system designers and developers. SPT introduces a quantifiable notion of time and resources. It annotates model elements with quantitative information related to time, information used for timeliness, performance, and schedulability analyses.

SPT only considers (chrono)metric time, which makes implicit reference to physical time. It provides time-related concepts: concepts of instant and duration, concepts for modeling events in time and time-related stimuli. SPT also addresses modeling of timing mechanisms (clocks, timers), and timing services. SPT, which relies on UML 1.4, had to be aligned with UML 2.1. This is one of the objectives of the MARTE profile, presented in Section ??.

Non OMG profiles Several "unofficial" UML profiles are also considering time modeling. We mention a few, developed for different purposes, as work related to ours.

EAST-EEA is an ITEA project on Embedded Electronic Architecture [START_REF]ITEA: EAST-ADL -The EAST-EEA Architecture Description Language[END_REF]. It provides a development process and automotive-specific constructs for the design of embedded electronic applications. Temporal aspects in EAST are handled by requirement entities. The concepts of Triggers, Period, Events, End to End Delay, physical Unit, Timing restriction, can be applied to any behavioral EAST elements. It is compliant with UML2.0, the intent is to deliver a UML2 profile.

The UML profile Omega-RT [START_REF] Graf | A real-time profile for UML[END_REF] focuses on analysis and verification of time and scheduling related properties. It is a refinement of the SPT profile. The profile is based on a specific concept of event making it easy to express duration constraints between occurrences of events. The concept of observer, which is a stereotype of state machine, is a convenient way for expressing complex time constraints. It would have to be aligned with UML2.0.

Summary The abovementioned profiles introduce relationships between Time and Events or Actions. They annotate the UML model with quantitative information about time. None consider logical and multiform time.

Allocation models

These are concerned with the mapping of application elements onto architectural platform resources and services. The following frameworks are currently untimed. It is in fact our main goal that a Time Model can be used to select and optimize such mapping according to the timing demands of both sides (and possibly additional real-time requirements).

UML deployments UML deployments consist in assigning concrete software elements of the physical world (artifacts) to nodes. Nodes can represent either hardware devices or software execution environments. Artifacts are physical piece of information-a file or a database entry-and model elements are stored in resources specified by artifacts. The MARTE allocation mechanism is complementary to the UML deployment mechanism, the differences are described in section ??. SysML allocation SysML [START_REF]OMG: Systems Modeling Language (SysML) Specification[END_REF] provides a mechanism to represent, at an abstract level, cross-associations among model elements with the broadest meaning. A SysML allocation is expected to be the precursor of more concrete relationships. It differentiates three of the many possible and not exclusive categories: behavior, flow and structure allocations. Behavior allocations separate the functions from the structure; they provide a way to allocate a behavior to a behavioral feature. Flow allocations have many usages; they include allocations of activity transitions (SysML flows) to connectors of structured activities (SysML blocks).

Structure allocations acknowledge the needs for a mapping relation of logical parts to more physical ones. The MARTE allocation is inspired from the SysML allocation and the differences are described in section ??. One reason for this choice is that we want to be able to define, in the most convenient way, how various durations and clock streams are connected in the course of the allocation. This can easily fit some of SysML constraints/parametrics and requirements modeling features, which were originally used to model physical constraints or uninterpreted requirement engineering information respectively.

Timed allocation models

We believe that suitable models for real-time and embedded systems design and analysis should support both time and allocation. We give here a brief insight of the Society of Automotive Engineer(SAE)'s Architecture Analysis & Design Language(AADL) standard [START_REF]SAE: Architecture Analysis and Design Language[END_REF].

The temporal semantics of AADL concepts is defined using "hybrid automata". These automata are hierarchical finite state machines with real-valued variables that denote the time. Temporal constraints, expressed as state invariants and guards over transitions, define when the discrete transitions occur. Concurrent executions are modeled using threads managed by a scheduler. The dispatch protocol (periodic, aperiodic, sporadic and background) determines when an active thread executes its computation. AADL supports multiform time models. However, it lacks model elements to describe the application itself, independently of the resources. UML activities allow for a description of the application, actions executed sequentially or concurrently, without knowing, at first, whether actions are executed by a periodic thread or a subprogram. This important information is brought by an orthogonal process, the allocation. After several iterations, analysis, the threads are eventually deployed (or bound) to the execution platform.

AADL offers a binding mechanism to assign software components (data, thread, process, etc.) to execution platform components (memory, processor, buses, etc.). Each software component can define several possible bindings and properties may have different values depending on the actual binding. This binding mechanism encompasses both the UML deployment and the MARTE allocation, while sometimes it is useful to separate the two concepts.

MARTE

MARTE is a response to the OMG RFP to provide a UML profile for real-time and embedded systems [START_REF]OMG: UML profile for Modeling and Analysis of Real-Time and Embedded systems (MARTE)[END_REF]. MARTE is a successor of SPT, aligned with UML 2, and with a wider scope. MARTE introduces a number of new concepts, including time and allocation concepts, which are central to this paper.

MARTE time model

Time in SPT is a metric time with implicit reference to physical time. As a successor of SPT, MARTE supports this model of time. However, MARTE goes beyond this quantitative model of time and adopts more general time models suitable for system design. In MARTE, Time can be physical, and considered as dense or discretized, but it can also be logical, and related to user-defined clocks. Time may even be multiform, allowing different times to progress in a non-uniform fashion, and possibly independently to any (direct) reference to physical time. Concept of time structure Figure ?? shows the main concepts introduced in MARTE to model time. This is a conceptual view, or in the UML profile terminology, a domain view. The corresponding UML representations will be presented later. The building element in a time structure is the TimeBase. A time base is a totally ordered set of instants. A set of instants can be discrete or dense. The linear vision of time represented by a single time base is not sufficient for most of the applications, especially in the case of multithreaded or distributed applications. Multiple time bases are then used. A MultipleTimeBase consists of one or many time bases. A time structure contains a tree of multiple time bases.

MultipleTimeBase

Time bases are a priori independent. They become dependent when instants from different time bases are linked by relationships (coincidence or precedence). The abstract class TimeInstantRelation in Figure ?? has CoincidenceRelation and PrecedenceRelation as concrete subclasses. Instead of imposing local dependencies between instants, dependencies can be directly imposed between time bases. A TimeBaseRelation (or more precisely one of its concrete subclasses) specifies many (possibly an infinity of) individual time instant relations. This will be illustrated later on some time base relations. TimeBaseRelation and TimeInstantRelation have a common generalization: the abstract class TimeStructureRelation. As a result of adding time structure relations to multiple time bases, time bases are no longer independent and the instants are partially ordered. This partial ordering of instants characterizes the time structure of the application.

This model of time is sufficient to check the logical correctness of the application. Quantitative information, attached to the instants, can be added to this structure when quantitative analyses become necessary.

Clock In real world technical systems, special devices, called clocks, are used to measure the progress of physical time. In MARTE, we adopt a more general point of view: a clock is a model giving access to the time structure. Time may be logical or physical or both. MARTE qualifies a clock refering to physical time as a chronometric clock, emphasizing on the quantitative information attached to this model. A Clock makes reference to a TimeBase. Clocks and time structures have mathematical definitions introduced below. This formal modeling is transparent to the user of the profile.

The mathematical model for a clock is a 5-tuple (I, , D, λ, u) where I is a set of instants, is an order relation on I, D is a set of labels, λ : I → D is a labeling function, u is a symbol, standing for a unit. For a chronometric clock, the unit can be the SI time unit s (second) or one of its derived units (ms, us. . . ). The usual unit for logical clocks is tick, but user-defined units like clockCycle, executionStep . . . may be chosen as well. To address multiform time, it is even possible to consider other physical units like angle degrees (this is illustrated in an application of our time model to an automotive application [START_REF] André | A multiform time approach to real-time system modeling: Application to an automotive system[END_REF]). Since a clock refers to a TimeBase, (I, ≺) is an ordered set.

A Time Structure is a 4-tuple (C, R, D, λ) where C is a set of clocks, R is a relation on a,b∈C,a =b (I a × I b ), D is a set of labels, λ : I C → D is a labeling function. I C is the set of the instants of a time structure. I C is not simply the union of the sets of instants of all the clocks; it is the quotient of this set by the coincidence relation induced by the time structure relations represented by R.

Time-related concepts Events and behaviors can be directly bound to time. The occurrences of a (timed) event refer to points of time (instants). The executions of a (timed) behavior refer to points of time (start and finish instants) or to segments of time (duration of the execution). In MARTE, Instant and Duration are two distinct concepts, specializations of the abstract concept of Time. TimedEvent (TimedBehavior, resp.) is a concept representing an event (a behavior, resp.) explicitly bound to time through a clock. In this way, time is not a mere annotation: it changes the semantics of the timed model elements.

MARTE Time profile

The time structure presented above constitutes the semantic domain of our time model. The UML view is defined in the "MARTE Time profile". This profile introduces a limited number of powerful stereotypes. We have striven to avoid the multiplication of too specialized stereotypes. Thanks to the sound semantic grounds of our styereotypes, modeling environments may propose patterns for more specific uses. The main sterotypes are presented in figures ?? to ??. ClockType is a stereotype of the UML Class. Its properties specifies the kind (chronometric or logical) of clock, the nature (dense or discrete) of the represented time, a set of clock properties (e.g., resolution, maximal value. . . ), and a set of accepted time units. Clock is a sterotype of InstanceSpecification. An OCL rule imposes to apply the Clock stereotype only to instance specifications of a class stereotyped by Clock-Type. The unit of the clock is given when the stereotype is applied. Unit is defined in the Non Fonctional Property modeling (NFPs) subprofile of MARTE, it extends EnumerationLiteral. It is very convenient since a unit can be used like any user-defined enumeration literal, and conversion factors between units can be specified (e.g., 1ms = 10 -3 s). TimedElement is an abstract stereotype with no defined metaclass. It stands for model elements which reference clocks. All other timed stereotypes specialize TimedElement.

Clock constraints

ClockConstraint is a stereotype of the UML Constraint. The clock constraints are used to specify the time structure relations of a time domain. In turn, these relations characterize the R relation of the underlying mathematical model of the time structure.

The context of the constraint must be a TimedDomain. The constrained elements are clocks of this timed domain and possibly other objects. The specification of a clock constraint is a set of declarative statements. This raises the question of choosing a language for expressing the clock constraints. A natural language is not sufficiently precise to be a good candidate. UML encourages the use of OCL. However, our clocks usually deal with infinite sets of instants, the relations may use many mathematical quantifiers, which are not supported by OCL. Additionnally, OCL [START_REF]OMG: Object Constraint Language, version 2.0[END_REF] is made to be evaluatable, while our constraints often have to be processed altogether to get a set of possible solutions. So, we have chosen to define a simple constraint expression language endowed with a mathematical semantics. The specification of a clock constraint is a UML::OpaqueExpression that makes use of pre-defined (clock) relations, the meaning of which is given in mathematical terms, outside the UML. Our Constraint Specification Language is not normative. Other languages can be used, so long as the semantics of clocks and clock constraints is respected. In UML, a Behavior describes a set of possible executions; an execution is the performance of an algorithm according to a set of rules. MARTE associates a duration, an instant of start, an instant of termination with an execution, these times being read on a clock. The stereotype TimedProcessing (Figure ??) extends the metaclasses Behavior, Action, and also Message. The latter extension assimilates a message tranfer to a communication action.

Note that, StateMachine, Activity, Interaction being Behavior, they can be stereotyped by TimedProcessing, and thus, can be bound to clocks.

MARTE allocation model

Allocation of functional application elements onto the available resources (the execution platform) is main concern of real-time embedded system design. This comprises both spatial distribution and temporal scheduling aspects, in order to map various algorithmic operations onto available computing and communication resources and services.

The MARTE profile defines application and execution platform models. A MARTE allocation is an association between a MARTE application and a MARTE execution platform. Application elements may be any UML element suitable for modeling an application, with structural and behavioral aspects. An execution platform is represented as a set of connected resources, where each resource provides services to support the execution of the application. So, resources are basically structural elements, while services are rather behavioral elements. Application and Execution platform models are built separately, before they are paired through the Allocation process. Often this requires prior adjustment (inside each model) to abstract/refine its components so as to allow a direct match. Allocation can be viewed as a "horizontal" association, and abstraction/refinement layering as a "vertical" one, with the abstract version relying on constructs introduced in the more refined model. While different in role, allocation and refinement share a lot of formal aspects, and so both are described here.

Application and Execution platform elements can be annotated with time information based on logical or chronometric clocks (Section ??). Allocation and refinement provide relations between these timings under the form of constraints between the clocks and their instants. Other similar non-functional properties such as space requirement, cost, or power consumption are also considered.

In MARTE, we use the word allocation rather than deployment (as in UML) since allocation does not necessarily imply a physical distribution and could simply represent a logical distribution or scheduling. Execution platform models can be abstract at some points and not necessarily seen as concretization models. For instance, two pieces of an algorithm could be allocated to two different processor cores, while the executable file containing both pieces would be deployed on the memory of the processor and the source file containing the specification of the algorithm would be deployed on a hard disk. This dual function was recognized in SPT, where allocation was called realization, while refinement was used as such. MARTE allocation and refinement are complementary to the UML deployment; we prefer to keep the three concepts separated. This is not the case of AADL that provides a single mechanism-the binding-for all three concepts. The allocation mechanism proposed by MARTE is actually very close to the structure allocations of SysML because it allocates logical parts to more physical ones. However, MARTE makes it explicit that both the logical and physical parts could be either of a behavioral or structural nature. Contrary to SysML, MARTE makes a difference between allocation-from application model elements to execution platform model elements-and refinement of an abstract model elements (logical or physical) into more specific elements.

The stereotype Allocate A MARTE allocation is materialized by the stereotype Allocate (Figure ??), which extends the UML metaclass Abstraction, and can be associated with NFP constraints. Allocation can be structural, behavioral, or hybrid. Structural allocation associates a group of structural elements and a group of resources. Behavioral allocation associates a set of behavioral elements and a service provided by the execution platform. When clear from context, hybrid allocations are allowed (e.g., when an implicit service is uniquely defined for a resource). At the finer level of detail, behavioral allocation deals with the mapping of UML actions to resources and services. The stereotype Allocated MARTE advocates the need to differentiate the potential sources of an allocation from the targets. Each model element involved in an allocation is annotated with the stereotype Allocated (as in SysML), which extends the metaclass NamedElement or rather one of its specializations (Fig- ure ??). The stereotype ApplicationAllocationEnd, noted by the keyword «ap allocated», denotes a source of an allocation. The stereotype ExecutionPlatformAllocationEnd, noted by the keyword «ep allocated», represents the target of an allocation. The stereotype Allocated is not abstract to ensure compatibility with SysML, but one of its specializations should be preferred. The property allocatedTo, respectively allocatedFrom, is a derived property resulting from the process of creating the abstraction (allocation); they facilitate the identification of the targets, respectively the sources, of the allocation when all model elements cannot be drawn on the same diagram.

Illustrative Examples

Chronometric clocks

The MARTE TimeLibrary provides a model for the ideal time used in physical laws: idealClk, which is an instance of the class IdealClock, stereotyped by ClockType (Fig. ??). idealClk is a dense time clock, its unit is the SI time unit s. Starting with idealClk, the user can define new discrete chronometric clocks (Fig. ??). First, the user specifies Chronometric-a class stereotyped by Clock-Type-which is discrete, not logical (therefore chronometric), and with a read only attribute (resolution). Clocks belong to timed domains. In Fig. ??, a single time domain is considered. It owns 3 clocks: idealClk, cc1 and cc2, two instances of Chronometric that both use s (second) as a time unit; and whose resolution is 0.01 s. The three clocks are a priori independent. A clock constraint specifies relationships among them.

The first statement of the constraint defines a clock c local to the constraint. c is a discrete time clock derived from idealClk by a discretization relation. The resolution of this clock is 1 ms. The next two statements specify that cc1 and cc2 are subclocks of c with a rate 10 times slower than c. The fourth and fifth statements indicate that cc1 and cc2 are not perfect clocks. Flaws are characterized by non functional properties like stability and offset. Their rate may have small variations (a stability of 10 -5 implicitly measured on idealClk). The last statement claims that the two clocks are out of phase, with an offset value between 0 and 5 ms measured on idealClk. Note that even if cc1 and cc2 look alike, they are not identical because relations are not necessarily functional.

AADL communication

To explain its port-based communication semantics, the AADL specification takes the example of a thread Read that captures a sample and sends it to a second thread Control. The two threads are assumed to be dispatched at the same time. Several cases are studied, the case where the two threads are dispatched with the same period, the case where Read is dispatched twice faster than Control (undersampling), and the case where Read is dispatched twice slower than Control (oversampling). These cases are studied first with an immediate communication (the output value is available as soon as the thread Read completes) and then with a delayed communication (the output value is available only at the next dispatch of the thread Read).

To compare our approach to AADL, we take the case of an immediate communication, which is the more challenging, with undersampling. As said before, the main difference of our approach is that we separate the application models from the execution platform models. The application is described with a UML activity diagram (Fig. ??) using purely logical clocks and stereotyped by «TimedProcessing». The behavior of Read and Control are executed repetitively, they communicate through a datastore object node that allows for multiple readings of the same sample. In a second step, the application is allocated to the model of an execution platform, a process containing two threads that communicate through a shared variable. In our model, t1 and t2, or rather their dispatch time, are considered as clocks. These two harmonic clocks are defined using a local 100Hz-clock c. Then t1 and t2 are derived from c with respective frequency 20Hz and 10Hz.

Additional clock constraints are associated with the allocate dependency to map the application clocks to the platform clocks. All these constraints define a partial order. In the case of a delayed communication, these would have been enough to have an equivalence of all possible schedulings. With an immediate communication, an additional constraint is required to guarantee the same behavior than AADL. This constraint would follow a greedy scheduling in order to execute Control as soon as possible. Our constraint model allows for delaying subjective choices as much as possible in order to avoid overspecification.

Conclusion

We presented a UML profile for comprehensive Time Modeling. Time here can be of discrete or dense, physical or logical. Logical time allows to model various time threads sustaining asynchronous or loosely time-related concurrent processes. This philosophy (of assigning logical clocks in order to explicitly handle time rates) borrows to foundational notions in embedded MoCC design. To this we add a kernel language of clock constraint relations, as well as timed events constraint relations. This constraint language, while currently simple, allows to define most useful clock relations (such as being periodic). While the profile can be considered as a "creative" translation of existing ideas on tagged systems to a UML setting (with all the alignments it required that were far from trivial), the clock constraint language and its use as a formal specification of classical time relation notions is original, to the best of our knowledge.

Time annotation can then be applied to behavioral elements, leading to TimedEvent and TimedProcessing, and to structural elements, leading to clocked Classes and clocked Objects. This can be performed on application models and architecture models of the embedded design. Then the system dynamics should run according to (partial) timing constraints, if possible, according to a timed operational semantics. Providing timed constructs in UML behavioral models (state diagrams and activity diagrams mostly) would be the next step here. Numerous examples exist (outside the UML) of timed languages and calculi under the form of MoCC constructors inside the proper time domain. Model transformation tools could extract the time properties, feed them into timing analysis tools and bring the result back into UML within a UML simulator. In that sense, our profile would give the time semantics of UML models.

Clock constraints provide partial scheduling information, and an actual schedule can be obtained by solving such a set of constraints, some of which originate from the application model, some from the execution platform model, and some from the system's real-time requirements. The same formalisms of clock relations can also be used in some case to represent the result of the scheduling decisions, and display them to the designer.

We provided modeling instances and case studies to illustrate and motivate the modeling framework. We showed how it allows to introduce a number of useful time predicates on events. We also showed the intent behind logical time by considering examples with various clocks running at unrelated speeds.

Fig. 1 .

 1 Fig. 1. Time structure (Domain view).

Fig. 2 .

 2 Fig. 2. MARTE TimeModeling profile: Clock.

Fig. 3 .Fig. 4 .

 34 Fig. 3. MARTE TimeModeling profile: TimedEvent.

Fig. 5 .

 5 Fig. 5. The stereotype «allocate».

Fig. 6 .

 6 Fig. 6. The stereotype «allocated».

Fig. 7 .

 7 Fig. 7. Ideal and Chronometric clocks.

Fig. 8 .

 8 Fig. 8. Clock constraints.

Fig. 9 .

 9 Fig. 9. Clock constraints.

http://dx.doi.org/10.1007/978-3-540-75209-7_38

a preliminary version is available at www.promarte.org


Lester Kwiatkowski
email: lester.kwiatkowski@lsce.ipsl.fr

James Orr

Diverging seasonal extremes for ocean acidification during the twenty-first century

 , particularly for pH. Here we assess the latter by analysing 9 Earth System Models (ESMs) forced with a business-as-usual emissions scenario 13 . During the twentyfirst century, the seasonal cycle of surface-ocean pH was attenuated by 16±7 %, on average, while that for hydrogen ion concentration [H + ] was amplified by 81±16 %. Simultaneously, the seasonal amplitude of aragonite saturation state (Ω arag ) was attenuated except in the subtropics where it was amplified. These contrasting changes derive from regionally varying sensitivities of these variables to atmospheric CO 2 and climate change and diverging trends in seasonal extremes in the primary controlling variables (temperature, dissolved inorganic carbon, and alkalinity). Projected seasonality changes will tend to exacerbate impacts of increasing [H + ] on marine organisms during summer and ameliorate impacts during winter, although the opposite holds in the high latitudes. Similarly over most of the ocean, impacts from declining Ω arag are likely to be intensified during summer and dampened during winter.

Ocean CO 2 uptake affects marine chemistry via ocean acidification [START_REF] Orr | Anthropogenic ocean acidification over the twenty-first century and its impact on calcifying organisms[END_REF][START_REF] Bopp | Multiple stressors of ocean ecosystems in the 21st century: projections with CMIP5 models[END_REF][START_REF] Doney | Ocean Acidification: The Other CO2 Problem[END_REF] , a process that increases concentrations of CO 2 , H + and HCO 3 -, and reduces levels of pH and CO 3 2-. Although much effort has been devoted to assessing the direct and indirect effects of increasing atmospheric CO 2 on the mean state of these ocean carbonate chemistry variables, few studies have addressed the corresponding changes in their seasonal cycles [START_REF] Mcneil | Southern Ocean acidification: A tipping point at 450-ppm atmospheric CO2[END_REF][START_REF] Sasse | Quantifying the influence of CO2 seasonality on future aragonite undersaturation onset[END_REF][START_REF] Mcneil | Future ocean hypercapnia driven by anthropogenic amplification of the natural CO2 cycle[END_REF] . The seasonal cycles of ocean carbonate chemistry variables are the result of variations in the seasonality of different physical and biological processes [START_REF] Takahashi | Climatological distributions of pH, pCO2, total CO2, alkalinity, and CaCO3 saturation in the global surface ocean, and temporal changes at selected locations[END_REF][START_REF] Hagens | Attributing seasonal pH variability in surface ocean waters to governing factors[END_REF] . Those for pCO 2 and pH are largely regulated by variations in temperature in the subtropics, while at higher latitudes their oscillations are typically dominated by biological uptake and release of CO 2 (photosynthesis and respiration). In contrast, temperature plays a minor role in controlling the seasonal cycles of the carbonate saturation state of seawater (Ω = [𝐶𝑎 !! ] [𝐶𝑂 !

!! ]/𝐾 !" ) even at lower latitudes; rather, it is the variability of total alkalinity and dissolved inorganic carbon that dominates [START_REF] Takahashi | Climatological distributions of pH, pCO2, total CO2, alkalinity, and CaCO3 saturation in the global surface ocean, and temporal changes at selected locations[END_REF][START_REF] Hagens | Attributing seasonal pH variability in surface ocean waters to governing factors[END_REF] . To survive, marine organisms must cope with variations in their local environment, however many may be highly sensitive to changes in ocean carbonate chemistry [START_REF] Kroeker | Meta-analysis reveals negative yet variable effects of ocean acidification on marine organisms[END_REF][START_REF] Mangan | Fluctuating seawater pH/pCO2 regimes are more energetically expensive than static pH/pCO2 levels in the mussel Mytilus edulis[END_REF] . Calcifying species such as echinoderms, byrozoans and cnidarians exhibit depressed calcification, growth and survival rates at lower Ω arag/calc (refs. [START_REF] Albright | Reversal of ocean acidification enhances net coral reef calcification[END_REF][START_REF] Kwiatkowski | Nighttime dissolution in a temperate coastal ocean ecosystem increases under acidification[END_REF][START_REF] Kroeker | Meta-analysis reveals negative yet variable effects of ocean acidification on marine organisms[END_REF] ). In teleost fish and marine invertebrates, ion exchange is reduced by extracellular acidosis or high external [H + ], depressing protein synthesis and metabolic rates [START_REF] Pörtner | Ecosystem effects of ocean acidification in times of ocean warming: a physiologists view[END_REF] . Physiological and behavioural functioning is also sensitive to pCO 2 , with high external concentrations impairing olfactory discrimination [START_REF] Munday | Ocean acidification impairs olfactory discrimination and homing ability of a marine fish[END_REF] and predator-prey responses [START_REF] Watson | Ocean acidification alters predator behaviour and reduces predation rate[END_REF] . Accounting for seasonal variability in carbonate chemistry influences the timing of the projected onset of CaCO 3 undersaturation [START_REF] Mcneil | Southern Ocean acidification: A tipping point at 450-ppm atmospheric CO2[END_REF][START_REF] Sasse | Quantifying the influence of CO2 seasonality on future aragonite undersaturation onset[END_REF][START_REF] Gruber | Rapid Progression of Ocean Acidification in the California Current 11 System[END_REF] , when waters become corrosive to pure aragonite (Ω arag <1) and calcite (Ω calc <1) (i.e., metastable and stable forms of CaCO 3 ). These seasonal variations also affect when surface waters will reach a proposed threshold, beyond which pCO 2 levels may become damaging [START_REF] Mcneil | Future ocean hypercapnia driven by anthropogenic amplification of the natural CO2 cycle[END_REF] . Here we explore how seasonality of surfaceocean [H + ], pH and Ω arag will respond to projected increases of atmospheric CO 2 and climate change during the twenty-first century. Unlike studies that have assumed unchanging seasonality, combining observational estimates of present seasonality (repeated in time) with model projections of the change in mean state [START_REF] Mcneil | Southern Ocean acidification: A tipping point at 450-ppm atmospheric CO2[END_REF][START_REF] Sasse | Quantifying the influence of CO2 seasonality on future aragonite undersaturation onset[END_REF] , we use an ensemble of 9 Earth System Models (ESMs) containing coupled ocean biogeochemistry schemes. Thus we assess how seasonality is affected by increasing concentrations of atmospheric CO 2 and climatechange driven changes in sea surface temperature and biology [START_REF] Bopp | Multiple stressors of ocean ecosystems in the 21st century: projections with CMIP5 models[END_REF]21 . Ocean biogeochemistry models (OBM) generally reproduce the amplitude and phase of observational estimates for seasonal air-sea CO 2 fluxes in the Pacific 22 , Atlantic [START_REF] Schuster | An assessment of the Atlantic and Arctic sea-air CO2 fluxes, 1990-2009[END_REF] and Indian Oceans [START_REF] Sarma | Sea-air CO2 fluxes in the Indian Ocean between 1990 and 2009[END_REF] while their skill in high latitude regions is more limited 23 ,25,26 . We found consistent results for the CMIP5 ESMs that include an OBM. The models broadly capture the zonalmean patterns of seasonal changes in [H + ] (r~0.8) and Ω arag (r~0.95) of observational climatologies (Supplementary Figs. 123456). Hence they appear to offer the best option to assess projected changes in seasonality during the coming century. Nonetheless, model performance in the Southern Ocean is particularly limited, with certain models negatively correlated with the [H + ] climatology, possibly due to excessive simulated warming in summer [START_REF] Lenton | Sea-air CO 2 fluxes in the Southern Ocean for the period 1990&ndash[END_REF] or underestimated winter convective CO 2 entrainment and the impact of biological CO 2 uptake [START_REF] Mongwe | The seasonal cycle as a mode to diagnose biases in modelled CO2 fluxes in the Southern Ocean[END_REF] . Projected trends in seasonality were evaluated for the business-as-usual (2006-2100) Representative Concentration Pathway 8.5 (RCP8.5) [START_REF] Riahi | RCP 8.5-A scenario of comparatively high greenhouse gas emissions[END_REF] relative to results from the historical simulation 27 (1990-1999). Changes in seasonality were determined by subtracting a cubic spline fit from the monthly time series in each grid cell and calculating the annual peak-topeak amplitude for each year of the detrended dataset. Both the mean state and seasonality of projected [H + ], pH and Ω arag change over the twenty-first century, as illustrated in Figure 1 for one model. During this century, the amplitude of seasonal cycle in [H + ] is projected to increase by 81±16 % (multi-model mean ± 1SD) (Fig. 2a). Increases in seasonal amplitudes of [H + ] are generally higher in the high latitudes, particularly in the Arctic where the average amplification is 147±57 % (Fig. 3a,S8). Yet unlike the seasonal amplitude for [H + ], that for pH is projected to decline globally, on average by 16±7 % during the twenty-first century (Fig. 2b). Attenuation is generally more intense in the low and mid-latitudes but also occurs over most of the highlatitude ocean (Fig. 3b,S8). Given that pH is directly related to [H + ], it is counterintuitive that while the seasonal amplitude in [H + ] increases, the seasonal amplitude in pH declines. However, the log transformation implies that

𝑑 𝑝𝐻 = -1 2.303 𝑑[𝐻 ! ] [𝐻 ! ] (1)
That is, the seasonal amplitude of pH depends not only on the seasonal amplitude of Regarding Ω arag , its global average seasonal amplitude is attenuated by 9±8 % during the twenty-first century (Fig. 3c). Attenuation can exceed 40 % in the temperate-to-polar zones, while in the subtropics, where the amplitude of the seasonal cycle of Ω arag is much smaller (Supplementary Fig. 7), there is amplification of up to 30 % (Fig. 3c), as discussed below. These projected changes in the seasonal amplitude of [H + ], pH and Ω arag result from nonidentical changes in both the seasonal maxima and minima (Fig. 1,S12).

To further investigate the causes of changes in seasonal amplitudes of derived variables [H + ] and Ω arag , we used 2 complementary approaches: (1) idealised simulations and (2) first-order Taylor-series deconvolution. The idealised simulations partition the geochemical versus radiative effects of increasing atmospheric CO 2 , where the geochemical effect is due to ocean carbon uptake and the radiative effect influences carbonate chemistry through rising temperatures and simultaneous changes in marine biological activity. The deconvolution quantifies how the seasonal amplitude of each derived variable (Δy), is affected by changes in temperature (T), salinity (S), dissolved inorganic carbon (C T ) and total alkalinity (A T ), i.e., four model variables used to calculate carbonate chemistry. That is for y = f(C T , A T , T, S),

∆𝑦 = 𝜕𝑦 𝜕𝐶 ! ∆𝐶 ! + 𝜕𝑦 𝜕𝐴 ! ∆𝐴 ! + 𝜕𝑦 𝜕𝑇 ∆𝑇 + 𝜕𝑦 𝜕𝑆 ∆𝑆 (2)
where the partial differentials are estimated numerically and ΔT, ΔC T , ΔA T and ΔS are the changes in input variables, synchronous with Δy, assuming other contributions are negligible. For the change in amplitude, Equation ( 2) is evaluated separately with decadal mean seasonal cycles for the first and last simulated decades of the RCP8.5 scenario, and then the latter is subtracted from the former. This deconvolution illustrates how the proximate drivers of seasonal amplification of [H + ] vary spatially. In the mid-to-high latitudes it is the residual effect of opposing increases in the terms for dissolved inorganic carbon ((∂H + /∂C T )ΔC T ) and total alkalinity ((∂H + /∂A T )ΔA T ) that dominates. However, in the low latitudes, changes in these two terms largely compensate, so it is the increase in the temperature term ((∂H + /∂T)ΔT) that dominates (Supplementary Fig. 9). Because the sensitivities of H + to C T and A T (partial differentials) are roughly equal and opposite, it is the balance between ΔC T and ΔA T that control the change in seasonal amplitude of [H + ] in the mid-to high latitudes (Supplementary Fig. 10). One cannot assume that ΔA T remains constant while only ΔC T will change. For instance, changes in ΔA T will be decoupled from those of ΔC T due to an altered hydrological cycle. Increased freshwater input dilutes C T and A T , but C T then tends to equilibrate with atmospheric CO 2 , unlike A T . Hence addition of low alkalinity freshwater reduces pH, despite the opposite tendency from dilution alone. The high latitudes will experience this effect most, from enhanced precipitation, ice melt, and river runoff. Decoupling will also result from anthropogenic CO 2 invasion and changes in primary production. In the low latitudes, while the C T and A T terms are small and compensating, the temperature term dominates, enhanced by a doubling of ∂H + /∂T (Supplementary Fig. 11). The ultimate drivers of this seasonal amplification in [H + ] are demonstrated by the idealised simulations, which show that it is the geochemical effect of increasing atmospheric CO 2 and consequently reduced buffer capacity [START_REF] Egleston | revisited: Buffer factors that quantify the response of ocean chemistry to changes in DIC and alkalinity[END_REF][START_REF] Hauck | Rising atmospheric CO2 leads to large impact of biology on Southern Ocean CO2 uptake via changes of the Revelle factor[END_REF] that is responsible for 92 % of global amplification, while the radiative effect provides minor reinforcement (Fig. 4,S13). For Ω arag, the proximate drivers of the general attenuation of its seasonal amplitude are a decline in the C T term ((∂Ω arag /∂C T )ΔC T ) which typically outweighs an opposing increase in the A T term ((∂Ω arag /∂A T )ΔA T ) (Supplementary Figs. 9-10). In the subtropics though, there is little change in the A T term, while the C T term increases due to a larger change in ΔC T , driving amplification of the Ω arag seasonal cycle in these regions. The ultimate driver of the seasonal attenuation in Ω arag is the geochemical effect of increasing atmospheric CO 2 which is responsible for >100 % of global attenuation, being partly offset by the radiative effect (Fig. 4,S13). In contrast, the subtropical amplification of the seasonal cycle of Ω arag results from the radiative effect driving enhanced amplification over the low latitudes in combination with the weaker attenuation from the geochemical effect in the subtropics. We have shown that under a business-as-usual emissions scenario, the seasonal variability of ocean carbonate chemistry is projected to change substantially during this century. Despite the diversity of OBMs in the multi-model ensemble [START_REF] Bopp | Multiple stressors of ocean ecosystems in the 21st century: projections with CMIP5 models[END_REF]21 , spatial patterns of the change in seasonal amplitude of [H + ], pH, and Ω arag are generally consistent (Fig. 3,S8). Previously it was shown that increasing atmospheric CO 2 will amplify the seasonal cycle of surface-ocean pCO 2 (ref. [START_REF] Mcneil | Future ocean hypercapnia driven by anthropogenic amplification of the natural CO2 cycle[END_REF] ), potentially resulting in earlier exposure to detrimental pCO 2 conditions for marine organisms. Here we show that increasing atmospheric CO 2 must also amplify the seasonal cycle of [H + ] in a similar manner. This is consistent with the near-linear relationship between [H + ] and pCO 2 for annual-mean trends during the twenty-first century [START_REF] Orr | Recent and future changes in ocean carbonate chemistry[END_REF] . Amplified [H + ] seasonality may worsen impacts from the long-term mean increase in [H + ], potentially resulting in earlier seasonal exposure to conditions that cause physiological acidosis and depress protein synthesis and metabolic rates in marine organisms. In the low latitudes, this enhanced exposure is most likely to occur during summer when warming drives the [H + ] seasonal high. In the high latitudes, enhanced exposure is most likely to occur when the effect of photosynthesis on [H + ] drawdown is limited [START_REF] Takahashi | Climatological distributions of pH, pCO2, total CO2, alkalinity, and CaCO3 saturation in the global surface ocean, and temporal changes at selected locations[END_REF][START_REF] Hagens | Attributing seasonal pH variability in surface ocean waters to governing factors[END_REF] . But amplified [H + ] seasonality will also diminish exposure to conditions that cause acidosis during seasonal lows, e.g., in winter months in the low-latitudes and during phytoplankton blooms in the high-latitudes. The seasonal amplitude of Ω arag is projected to amplify in some regions and attenuate in others. Attenuation dominates throughout most of the ocean owing to increases in aqueous carbon dioxide [CO 2 *], which reduces carbonate ion [CO 3 2-] and hence the buffer capacity. In the subtropics though, the seasonal amplitude of Ω arag increases because amplification driven by the radiative effect of CO 2 dominates the locally weak geochemical effect. The general attenuation of the seasonal amplitude of Ω arag is likely to exacerbate the impact of declining Ω arag during the summer high while dampening the impact of declining Ω arag during the winter low. The same processes that will affect future seasonal variability, particularly the direct geochemical effect from the atmospheric CO 2 increase and the corresponding indirect effect from radiative warming, are likely to affect future diurnal variability. Indeed we estimate an amplification of the diurnal cycle of [H + ] (122%) and an attenuation of the diurnal cycle of Ω arag (20%) that are similar to our estimates for the seasonal cycle, based on differences in observations of diel pH variability reported for two adjacent sites in the Bay of Naples, a control station and a station where natural venting of pure CO 2 has perturbed oceanic pCO 2 to reach levels expected for the late twenty-first century (Table S2; ref. [START_REF] Kerrison | Assessment of pH variability at a coastal CO2 vent for ocean acidification studies[END_REF] ). Future research should assess how altered carbonate chemistry variability on both diurnal [START_REF] Schulz | Diurnal changes in seawater carbonate chemistry speciation at increasing atmospheric carbon dioxide[END_REF][START_REF] Jury | Buffer Capacity, Ecosystem Feedbacks, and Seawater Chemistry under Global Change[END_REF] and seasonal timescales will affect marine organisms, especially those suspected to be vulnerable to ocean acidification. The diversity in projected changes in seasonal extremes of [H + ], pH, Ω arag and pCO 2 emphasizes the need to improve our understanding of the mechanisms that control how specific marine organisms are affected by ocean acidification. In particular, we will need to study the sensitivity of marine organisms to these simultaneous yet contrasting changes in seasonality to be able to assess aggregate effects on marine communities.

Methods

Earth System Models

Monthly surface-ocean carbonate chemistry fields were computed from monthly output of 9 CMIP5 models (Table S1) from prognostic fields for total alkalinity, dissolved inorganic carbon, temperature, salinity, and total dissolved inorganic phosphorus and silicon. Calculations were made offline using the mocsy package and the equilibrium constants recommended for best practices 35 . Output fields were regridded to a regular 1° x 1° regular grid to facilitate multi-model intercomparison. All quoted error bars represent one standard deviation of the multi-model mean. Model evaluation CMIP5 seasonal climatologies constructed from 1995-2004 model output years were compared against the Takahashi et al., 2014 (ref. [START_REF] Takahashi | Climatological distributions of pH, pCO2, total CO2, alkalinity, and CaCO3 saturation in the global surface ocean, and temporal changes at selected locations[END_REF] ) observational climatologies of [H + ], pH, pCO 2 and Ω arag (Supplementary Figs. 123456). Model output was regridded to the Takahashi 4° x 5° grid with the same ocean mask applied. The models generally capture the zonal-mean patterns of seasonality for observed climatologies of [H + ], pH, pCO 2 and Ω arag . The multi-model ensemble encompasses the observed seasonal variance for Ω arag yet overestimates the seasonal variance of [H + ] and pCO 2 (Supplementary Figs. 12). This overestimation is driven by the zonal-mean component of seasonal variance (Supplementary Figs. 12). Across all carbonate chemistry variables, models have high correlation coefficients for the zonal-mean component of seasonal variability and relatively low correlation coefficients for the zonal-anomaly component of seasonal variability. Model performance is generally best in the subtropics and worst in the Southern Ocean with respect to both [H + ] and Ω arag (Supplementary Figs. 3456). Yet in the Southern Ocean, the data used to construct the climatologies are typically summer biased.

Idealised simulations

Three out of the 9 models also ran idealised simulations that allowed us to separate the geochemical effect from the CO 2 increase from the radiative forcing effect of the same CO 2 increase. More precisely, we used results from three CMIP5 experiments: 1pctCO2, esmFixClim1 and esmFdbk1. Although these simulations are not directly comparable to those with the RCP8.5 scenario due to different simulation lengths and atmospheric CO 2 concentrations, they provide the only means of separating the ultimate geochemical and radiative drivers of seasonality change. In the 1pctCO2 simulations, the atmospheric CO 2 concentration increases from 280 ppm by 1 % per year reaching a doubling (2xCO 2 ) after 70 years (560 ppm) and quadrupling (4xCO 2 ) after 140 years. In the esmFixClim1 simulations, the atmospheric CO 2 concentration follows that of the 1pctCO2 simulations while the radiative module of each model experiences a constant atmospheric CO 2 concentration of 280 ppm. Conversely, in the esmFdbk1 simulations, the atmospheric CO 2 concentration is held constant at 280 ppm but the radiative module of each model experiences the same CO 2 concentration as the 1pctCO2 simulations. The mean response of the models in the 1pctCO2 simulations is similar spatially to that of the multi-model ensemble in RCP8.5 simulations (Figs. 3,4). This confirms that atmospheric CO 2 emissions are the driver of patterns of carbonate chemistry seasonality change and validates the use of the esmFixClim1 and esmFdbk1 simulations to partition the radiative and geochemical influences of CO 2 . It should be noted that there are limited increases in ocean temperatures in the esmFixClim1 simulations that result from changes associated with the terrestrial biosphere, for which elevated CO 2 reduces stomatal conductance, which in turn drives greater surface sensible heat fluxes and thus slight increases in temperatures 36 .

Taylor-series deconvolution

The first-order Taylor-series deconvolution was performed for [H + ] and Ω arag independently with output from the RCP8.5 simulations (eqn. 2). The partial differential terms were estimated numerically using the mocsy package and ΔT, ΔC T , ΔA T and ΔS represent the change in input variables synchronous with Δy. This approach reproduces the changes in the seasonal amplitude of each of the derived variables [H + ] and Ω arag to within much less than 1 % as shown in Figure S9. With the exception of the very high latitudes, the deconvolution was broadly consistent across the multi-model ensemble. The zonal-mean influence of the different terms is given in the supplementary material for the representative GFDL-ESM2M model (Supplementary Figs. 9-11).

Data availability

Figures Figure 1 .

 1 Figures

Figure 2 .Figure 4 .

 24 Figure 2. Relative change in the seasonal amplitude of carbonate chemistry variables with rising atmospheric CO 2 . Global anomaly in the seasonal amplitudes of a, [H + ] b, pH and c, Ω arag relative to mean 1990s values as a function of atmospheric CO 2 .

  All the CMIP5 ESM model data are available via the Earth System Grid Federation (ESGF). The derived data that support the findings of this study are available from the corresponding author upon request. References 35. Dickson, A. G., Sabine, C. L. & Christian, J. R. Guide to Best Practices for Ocean CO2 Measurements. (North Pacific Marine Science Organization, 2007). 36. Sellers, P. J. et al. Comparison of Radiative and Physiological Effects of Doubled Atmospheric CO2 on Climate. Science 271, 1402-1406 (1996).

Acknowledgements

This study was funded by the H2020 CRESCENDO grant (ref 641816) and the ERC IMBALANCE-P synergy grant (ref 610028). We acknowledge the World Climate Research Programme's Working Group on Coupled Modelling, which is responsible for CMIP. For CMIP the US Department of Energy's Program for Climate Model Diagnosis and Intercomparison provided coordinating support and led the development of software infrastructure in partnership with the Global Organisation for Earth System Science Portals. To analyse the CMIP5 data, this study benefited from the IPSL Prodiguer-Ciclad facility, which is supported by CNRS, UPMC, Labex L-IPSL which is funded by the ANR (ref ANR-10-LABX-0018) and by the European FP7 IS-ENES2 project (ref 312979). We thank B. Le Vu for preliminary discussions.

Author contributions

Both authors conceived this study, J.O. produced the derived variables, and both authors performed the analysis and wrote the manuscript, with L.K. leading the process.

Additional information

Correspondence and requests for materials should be addressed to L.K.

Competing financial interests

The authors declare no competing financial interests