## 1 Introduction  
Water availability has been shown to have dominant or co-dominant effects in the productivity of most terrestrial biomes on Earth [1, 2]. This is particularly true today of Mediterranean-type (MT) climate areas and will become crucial with global climate change [3, 4]. In these areas, natural vegetation has to cope with a strong seasonality of environmental conditions. The five relatively small, isolated regions of the world with Mediterranean-type climate, _i.e._, respectively parts of the Mediterranean Basin, California, South-Western and Southern Australia, Central Chile and Southern Africa, are approximately located between latitudes ranging from both 30\({}^{\circ}\) to 43\({}^{\circ}\) North and South with a total area of about 2.75 Mkm\({}^{2}\). The Mediterranean-type climate can be coarsely considered as a transition between dry tropical and temperate climates. They are characterized by a distinctive annual climate sequence in which a hot dry summer alternates with a cool to cold, humid period lasting of 5-10 months from fall through winter to spring. In these five regions, vegetation is dominated by short to tall shrubs or trees with small, evergreen, sclerophyllous leaves [5]. These shrubland and woodland formations are fairly similar in their physiognomy and provided the ideal testing vegetation type for studying low productive ecosystems with evergreen cover that undergo severe water limitations during the growing season. They also constitute a good model region for evaluating the generality of plant functions in the so-called evergreen broadleaf forests (EBF) of the Global International Geosphere-Biosphere Programme (IGBP) land classification that grow in some subtropical areas. Terrestrial ecosystems affect carbon dioxide (CO\({}_{2}\)) fluxes to and from the atmosphere through an exchange between gross primary production (GPP) and whole respiration. The net balance determines whether an ecosystem is sequestrating carbon (C) or releasing it into the atmosphere. This balance regulates C sink strength or net ecosystem productivity and changes continuously with climate drivers. Forest ecosystems are a major sink in the global carbon cycle, sequestrating large amounts of carbon annually and thus slowing the rise of CO\({}_{2}\) concentration in the atmosphere. Forests store ca. (standard abbreviation for latin allocation \"circa\", which means \"around\") 45% of terrestrial carbon and are responsible for half of terrestrial net primary production (quoted by [6]). Unfortunately, measuring and describing how trees whatever their functional type transfer C from the atmosphere into terrestrial biomass remains poorly quantified. We observe a lack of mechanistic understanding on this question and [7] suggest developing generalizable models of C allocation to biomass growth of plant parts, respiration, nonstructural C reserve, reproduction and defense, as a challenging endeavor. Global modeling, remote sensing and ecosystem flux derived from eddy-flux towers have demonstrated that climate and climate variations influence biogeochemical processes that control net ecosystem productivity at multiple timescales. The C sink strength is affected by differential sensitivity of respiration components and storage in both short- and long-lived C pools with environmental drivers. The MOD17A2 product is one of the primary sources of remote sensing-based GPP at global scale. It provides an 8-day mean GPP at 1 km spatial resolution for the entire land surface [8]. However, several recent studies have highlighted limitations of this model [9, 10, 11]. GPP MOD17A2 (further called GPP MODIS) is an extension of the light use efficiency (LUE) model of Monteith previously used for estimating net primary production [12, 13], where minimum temperature \(\mathrm{T_{min}}\) and vapor pressure deficit VPD were retained as the two scalars directly modifying maximum LUE, \(\mathrm{LUE_{max}}\)[14].