Impacts of scenarios RCP4.5 and RCP8.5 on plant physiology in Tapajos National Forest in the Brazilian Amazon using the ED2.2 model

ABSTRACT Models that simulate the process of stomatal conductance (gs) for a given set of environmental conditions are important, as this process is the main mechanism that controls the gas exchange of terrestrial plants absorbing atmospheric CO2 in tropical forests. Simulations were performed for the Tapajós National Forest, in the western Brazilian Amazon, observing the gs process under the current climate scenario (control) and under the scenarios RCP4.5 and RCP8.5 (2071 - 2100), using the ED2.2 ecosystem demography model. The results showed that the lower availability of soil water for the plants reduced photosynthesis due to the closing of the stomata. The model results for gross primary productivity (GPP) are similar to those observed in the field, varying about ≈24 MgC ha-1 year-1 for the rainy season and ≈23 MgC ha-1 year-1 for the dry season (average 2002 to 2010) in the control scenario. In the RCP4.5 scenario, simulated GPP was 30.7 and 30 MgC ha-1year-1 for the rainy and dry season, respectively (30.5 and 25 MgC ha-1year-1, respectively, for the RCP8.5 scenario). Our results also show that there may be a limitation on the increase in biomass carbon with the concentration of CO2, as GPP was lower in RCP8.5, despite this scenario having a higher value of atmospheric CO2 relative to RCP4.5.


INTRODUCTION
Over the past two decades, an increase of 0.2 °C per decade in the Earth´s surface temperature has been observed, leading to global climate change (Hawkins et al. 2017).Although the climate varies naturally over time and space, the observed temperature increase has been much faster than the pace recorded over glacial and interglacial cycles, and the best explanation for this increase is the accumulation of greenhouse gases in the atmosphere, mainly due to the increase in the concentration of atmospheric CO 2 (Nobre et al. 2007).
Climate change scenarios such as RCP4.5 and RCP8.5 (RCP, Representation Concentration Levels) have been used in numerous simulations, as they project a future with a higher concentration of atmospheric CO 2 (Lyra et al. 2016).The climate projections used in this study were obtained from the forced ETA model with the outputs of the English global model HadGEM3 by Chou et al. (2014).The ETA model was developed at the University of Belgrade and is used by INPE for forecasting weather (Bustamante et al. 1999) and climate (Chou et al. 2005).The Eta-HadGEM2-ES Regional Climate Model provides a set of climate projections (RCP's) for South America for the period 1960-2005 (present climate) and 2070-2099 (future projections).
The consequences of the increase in CO 2 have been investigated in several studies.An increase in CO 2 levels can affect plant physiology, causing stomata to open less with high concentrations of CO 2 (Field et al. 1995), which directly reduces the flow of moisture to the atmosphere (Sellers et al. 1996).In rainforest regions like the Amazon, where a significant portion of the moisture for precipitation comes from surface evaporation, the reduction of stomatal opening can also contribute to a decrease in precipitation, resulting in reduced soil moisture and surface and subsurface runoff, leading to a reduction in river flow and the so-called hydrological drought, in addition to meteorological drought (Betts et al. 2004;Liberato et al. 2010).There are four possible effects of drought in a tropical forest: (a) xylem embolism, which affects the carbohydrate transport capacity of trees (McDowell et al. 2011;Anderegg et al. 2012); (b) hydraulic fatigue (Rowland et al. 2015); (c) continuous reduction of carbohydrate reserves (Doughty et al. 2015); and (d) an increase of the fragility of the system with each drought, known as the degradation hypothesis (Franklin et al. 1985).
Another effect that the accumulation of CO 2 in the atmosphere causes is the retention of infrared radiation emitted from the Earth's surface after the absorption of sunlight, leading to a continuous increase in global surface temperatures (Zandalinas et al. 2021).This heating can reduce vegetation growth, altering the thermal environment of plants (Piao et al. 2009;Ficklin and Novick 2017).The temperature increase predicted by the Intergovernmental Panel on Climate Change (IPCC) scenarios can increase the evapotranspiration, leading to a reduction in soil moisture (Liberato et al. 2010).
Vegetation dynamics models that simulate the effects of climate change on tropical forests are becoming increasingly robust, by including the interactions of biophysical, physiological and structural parameters with meteorological variables (Saleska et al. 2009;Islam et al. 2021).One such simulation framework is the terrestrial biosphere model ED2.2 (Ecosystem Demography), which considers the heterogeneity of the ecosystem, increasing the capacity of the model to simulate the differential growth of plants as a function of size, age, density, leaf area etc. (Moorcroft et al. 2001).
Our objective was to evaluate the effect of scenarios RCP4.5 and RCP8.5 on stomatal conductance and gross primary productivity in the ED2.2 model for a tropical forest area in the Amazon.

Study area
The modeling simulation was carried out for an area (acronym FNT/K67) of the conservation unit Tapajós National Forest (Flona Tapajós), an area of 590,000 ha located at km 67 of the BR-366 highway, in the state of Pará (54º58'W, 2°51'S), Brazil.Most rainfall occurs between January and June (rainy season), with little or no rain in the dry season (De Souza et al. 2017).

The model
The Ecosystem Demography model (ED2.2) simulates the dynamics of continental ecosystem structure and functioning on a local scale, representing the population of trees.The model was built with a hierarchical structure that represents the physical and biological heterogeneity of the ecosystem, dividing the domain of interest into polygons (Longo et al. 2016).In each polygon, the meteorological forcing above the canopy is spatially uniform.The number of polygons is determined at the beginning of the simulation and is fixed in time.Each polygon is subdivided into "Sites".Each "Site" is subdivided into "Patches".Within each "Patch", there are structures called "Cohorts", which are groups of trees with different sizes and population densities (Figure 1).

Input data
For the initial configuration of the model, we used three types of input data: (I) atmospheric conditions (meteorological data), (II) edaphic conditions (data on soil properties); and (III) initial state of the vegetation (forest inventory data), which are described below.
Meteorological data -Specific air temperature (K) and humidity (kg kg -1 ), molar fraction of CO 2 (µmol mol -1 ), air pressure (Pa) above the crown, precipitation rate (kg m 2 s -1 ), solar radiation flux and long wave radiation incident on the ACTA AMAZONICA surface (W m -2 ), and horizontal wind speed (m s -1 ) were obtained for 2002-2009 from a micrometeorological station (hourly data) located within Flona Tapajos.
Soil relative humidity (%) was calculated for each layer using equation 1.
[1] where υ is the soil moisture for layer k, is the residual soil moisture (m 3 w.m -3 ) and is the porosity.
The soil hydraulic parameters, porosity, matrix potential for porosity, wilting point, logarithmic slope of the water retention curve and hydraulic conductivity, were derived from pedotransfer functions based on soil granulometry (Cosby et al. 1984).The flow of water between soil layers occurs in the liquid phase and was determined by Darcy's law (Bonan 1996).The field capacity in the model was calculated based on the equation of Clapp and Hornberger (1978).Permanent wilting point and residual soil moisture were defined as the soil moisture at which the soil matrix potential is equivalent to -1.5 and -3.1 Mpa, respectively (Longo et al. 2016).
The values of matrix potential at saturation and soil moisture at saturation fluctuate both seasonally and with soil depth according to the volume of rainfall that recharges the system.Despite defining a moisture value at the beginning of the simulations, the value of these parameters will vary with soil moisture.
Plant productivity -Forest inventory data from Flona Tapajós were obtained from Espírito-Santo et al. (2005).They are leaf area index, tree height and density observed at six transects per hectare.Gross primary productivity (GPP) is the vegetation's ability to capture atmospheric CO 2 while losing some of this assimilated CO 2 through autotrophic respiration (Silva 2013).In the ED2.2 model, GPP (kg C plant -1 s -1 ) was calculated using equation 2. Plant respiration (kg C plant -1 s -1 ) is calculated with equation 3: Plant physiology -The stomatal conductance (gs) for C3 plants was calculated according to Leuning (1995) using equation 4. The gs controls water loss and the CO 2 assimilation rate (m s -1 ).ACTA AMAZONICA and is the intercellular water vapor concentration, assumed to be at saturation (Medvigy et al. 2009).
The water limitation in the model was calculated according to equations 5 and 6 (Medvigy et al., 2009).
[5] [6] where A net = instantaneous rate of photosynthesis (mol c m -2 leaf -1 ); net = plant evapotranspiration (mol w m -2 leaf -1 ). ) is given by equation 7. The radiation in the model is solved using a multi-layer version of the two-stream model applied to three broad spectral bands: photosynthetically active radiation (PAR, wavelengths between 0.4 and 0.7 µm), near-infrared radiation (NIR, wavelengths between 0.7 and 3.0 µm) and thermal infrared radiation (TIR, wavelengths between 3.0 and 15 µm (Longo et al. 2016).The evaporation rates between the leaf and soil surface with canopy air space are regulated by two factors, the aerodynamic resistance and the effective vapor pressure deficit (VPD) between the respective surfaces and the air space.The variables related to water flow in the model are precipitation, runoff, throughfall, transpiration, leaf interception, wood interception and drainage.The allometric equation that defines root depth relative to tree height in ED2.2 is given by the simplified exponential function: , [8] where DBH = tree diameter at breast height (cm).

Simulations
To assess the equilibrium state of the vegetation biomass, simulations were performed to adjust the initial conditions to the model's equations, in a process called spin-up (Yang et al. 1995).The model ran for a spin-up period of 300 years.To assess the equilibrium state of the forest, we assumed that the last 30 years of simulation corresponded to quasi-equilibrium conditions.The non-instability of the model was assessed through the analysis of the seasonality of soil moisture, GPP and gs in relation to the field observations (Restrepo-Coupe et al. 2013;Nepstad et al. 2013;Da Rocha et al. 2004).After the simulations for the control scenario, scenarios RCP4.5 and RCP8.5 were simulated in the model.
To simulate the rainfall and air temperature conditions for Flona Tapajós projected by the RCP scenarios, a descriptive statistical analysis was performed comparing two time intervals from the Eta-HadGEM2-ES model: 1960-2005 (historical data) and 2070-2099 (model projections).The comparison showed an increase in air temperature and a reduction in rainfall (Table 1).After defining the values in Table 1, they were used to change the model's input data.For example, the RCP4.5 scenario estimate an increase in air temperature of 4°C, so we add 4°C to the monthly values.For rain and specific humidity, the data were also modified according to increase (+) or decrease (-).In RCP4.5 we kept the CO 2 concentration at 650 ppm and in RCP8.5 at 1100 ppm, with a constant value of longwave radiation for each scenario.The specific humidity (q) was calculated using temperature and relative humidity and its variation between the periods was assessed through descriptive statistics.The run time chosen for the simulations with the RCP4.5 and RCP8.5 scenarios was nine years, based on the simulated equilibrium data, generating new data for the interval from 2002 to 2010.The initial condition of soil moisture distribution was used as the simulations control for vegetation dynamics.Validation was performed with soil moisture data obtained in the field by Nepstad et al. (2013) for January 2002 to December 2004.Part of the water that reaches the ground through the leaves (throughfall) dripping and run-off from the wood (wood interception) runs off the surface and the rest seeps into the soil (drainage).
The radiation budget is solved using a multi-layer version of the two-stream model applied to three broad spectral bands: photosynthetically active radiation (PAR, wavelengths between 0.4 and 0.7 µm), near-infrared radiation (NIR, ACTA AMAZONICA wavelengths between 0.7 and 3.0 µm) and thermal infrared radiation (TIR, wavelengths between 3.0 and 15 µm (Longo et al. 2019).

Soil moisture
The vertical profiles of moisture represented well the annual variability of soil moisture observed in the field (R 2 = 0.89) (Figure 2).The seasonal pattern of soil moisture responded to precipitation.The ED2.2 model values for soil moisture were similar to the observed data, but the differences were larger in deeper layers (from layer 5 downwards).The reason could be that the soil was classified as a mineral in the ED2.2 model, although the soil in the study area contains organic matter and macropores (Furtado Neto et al. 2013).
In this version of the model organic matter in the soil is not taken into account.
In the control scenario, the moisture was recharged throughout the profile to the deeper layers as soon as the rainy season began (Figure 3a).In the RCP4.5 scenario, there was a reduction in soil moisture, especially in the deeper layers, most markedly around 8 m, with values around 0.25 m 3 m -3 (Figure 3b).
The moisture reduction in the layers around 5 m indicates the depth at which absorption of water by plant roots is greatest at these levels.The reduction of soil moisture occurred due to the reduction in rainfall, the only entry of water into the system.In the RCP8.5 scenario, the deeper layers remained with humidity below 0.25 m 3 m -3 , providing humidity for plant roots up to 4 m deep (Figure 3c).The distribution of the roots in the model reached up to 5 m deep, which may explain the greater dryness around this depth.In the ED2.2, the allometric equations assume that smaller trees have shallower roots than larger trees.As a result, during years of normal rainfall, the soil moisture is recharged down to the deeper soil layers during the wet season and is an important source of water for taller trees during the dry season.As the model allows the presence of roots in several layers, they have a uniform distribution along the profile, which is not supported by field data, due to the limited information on root structure at the species level for the Amazon.
The vapor pressure deficit was positively correlated with the higher soil matrix potential (R 2 = 0.85), suggesting that water stress reduced the ecosystem's efficiency in using available water.
For the control scenario, the transpiration simulated by the model was 75.7 mm month -1 in the rainy season and 83.9 mm month -1 in the dry season (Table 2).In the RCP4.5 scenario, transpiration was 52.5 mm month -1 in the rainy season and 73.9 mm month -1 in the dry season, while the respective values in the RCP8.5 scenario were 51.1 and 62.5 mm month -1 .The amount of water lost by transpiration in the model, is considered to be exactly equal to the amount of soil water brought into the intercellular space of the leaf through the plant's vascular system.
The decrease in rainfall in the two RCP scenarios had a direct effect on the generation of runoff (Table 2).In the three scenarios, transpiration increased from mid-March and May, when the amount of water available to the plant in the soil reached the maximum peak of the season.As transpiration increases and peaks around September, the water available to the plant gradually decreases and peaks at a minimum around September as well.The lowest transpiration value in the rainy season was recorded approximately two months after the water available to the plant reached its minimum (end of the dry season).In scenarios RCP4.5 and RCP8.5, there was   2) as the severity of the drought increased.

GPP and sensitive and latent heat flow
The simulation resulted in a GPP of 25 ± 0.76 Mg C ha -1 year -1 , close to the value of 25.6 Mg C ha -1 year -1 obtained for Tapajós by Restrepo-Coupe et al. (2013).In the three simulations, GPP hourly averages were higher between 11:00 and 13:00 (Figure 4a) when PAR reached maximum values.The correlation coefficient between GPP and PAR was R 2 = 0.9 for all scenarios.GPP reached higher values in the RCP8.5, followed by RCP4.5 and the control scenario (Figure 4a).GPP varied most markedly between seasons in the RCP8.5 scenario.Monthly average soil water storage explained about 50-60% of the variation in GPP (R 2 = 0.46, 0.5 and 0.6 for the control, RCP4.5 and RCP8.5 scenarios, respectively).These results are similar to published studies using the ED2.2 model (Longo et al. 2016).Powell et al. (2013) showed that the GPP data simulated by the ED model for the Tapajós area was underestimated.This can be explained, perhaps, by the fact that seasonality in the model does not yet capture the drop in productivity during the transition from the dry to the rainy season.However, despite these details that are still under study, the model reasonably represents what would be expected in terms of GPP for the study site.
The simulated GPP for the RCP4.5 and RCP8.5 scenarios was 30.7 and 30.5 Mg C ha -1 year -1 for the rainy season, and 30 and 25 Mg C ha -1 year -1 for the dry season, respectively.Our simulated values for gs during the day significantly decreased from 16:00 (Figure 4b).VPD was higher in the RCP4.5 and RCP8.5 than in the control scenario (Figure 4d).The equation for gs used in the model is regulated by the vapor pressure deficit, which explains the opposite behavior between gs and VPD.GPP was strongly correlated with gs (R 2 ~ 0.9 in all the Table 2. Average of water balance components (mm month -1 ) for the control scenario and the RCP4.5 and RCP8.5 simulated climate-change scenarios in Tapajós National Forest in the dry and rainy over a period of nine years (2002 -2010).ACTA AMAZONICA three scenarios).When the leaf temperatures were higher, gs tended to be lower (Figure 4b,c).The lowest gs values were observed for the RCP8.5, followed by the RCP4.5 scenario.VPD was highest between 12:00 and 15:00 (Figure 4d).In the control scenario, the maximum values of VPD were around 2.5 kPa and they are higher in the rainy season (Figure 4d).

Variable
The latent heat flux decreased and the simulated sensible heat flux increased, both in the dry and rainy season (Table 3), responding to the increase in CO 2 concentration and increase in air temperature.

DISCUSSION
Our results from the ED2.2 model showed that the reduction in precipitation under the conditions of the RCP4.5 and RCP8.5 scenarios can directly impact soil moisture.Severity was accentuated in the RCP8.5 scenario, despite higher atmospheric CO 2 concentration and increase in water use efficiency, indicating that a drier and warmer climate can limit vegetation growth.The variability in water availability can affect tree growth rates, since precipitation is the main source of soil moisture and, consequently, of water for vegetation and the values of soil hydraulic parameters depend on soil granularity (Longo et al. 2019).In the model, for any soil moisture, the hydraulic conductivity tended to be higher for sandy than for clayey soils.However, as clay particles are smaller, the soil matric potential reaches the wilting point much faster in clayey soils.In addition, the hydraulic conductivity is much lower for sandy soils than for clayey soils at the same matric potential (Longo et al. 2019).
The reduction of rainfall can potentially lead to a lower entry of water into the soil, increasing the matric potential.This matric potential indicates the effort that the plant will make to extract water from the soil, and stomatal conduction is directly related to this variable through a factor on a phenomenological scale ( ) ranging from 0 (no stress) to 1 (maximum stress) (Longo et al. 2016).
Decreased soil water reduced stomatal conductance and transpiration in scenarios RCP4.5 and RCP8.5.This behavior is a result of increased water stress, increased vapor pressure deficit and increased air temperature (Longo et al. 2016).In nature, stomatal closure blocks the flow of CO 2 to the leaves, affecting the accumulation of photoassimilates, which can reduce productivity (Paiva et al. 2005).Simulations  of the precipitation in the Amazon (Kooperman et al. 2018).Therefore, in addition to the decreased reduction in forest growth that is directly linked to the reduction in CO 2 absorption, the lower stomatal conductance in the Amazon reduces local evapotranspiration, directly impacting precipitation.In the field data from the study site, gs decreased between 15:00 and 16:00, and gs decreases with increasing leaf temperature (Felsemburgh 2009).
The increase in VPD with ambient temperature can affect photosynthesis, leading to the closing of stomata, reducing transpiration and, with it, decreasing CO 2 assimilation and photosynthetic rate (Lloyd and Farquar 2008).This result was obtained by Felsemburgh (2009) in Tapajós.In tropical forests, in the dry season, VPD is less than ~0.2 kPa and can increase to ~0.7 kPa in the rainy season (Rocha et al. 2014).When the VPD increased with temperature, the GPP decreased due to the decrease in soil water.This sensitivity to temperature rise is not the same for all species, due to differences in photorespiration rates.In C3 plants, CO 2 assimilation depends on carbon gain via the bifunctional enzyme Rubisco (oxygenase/carboxylase) and CO 2 loss via photorespiration and mitochondrial respiration (Braga et al. 2021).Thus, increased photorespiration and mitochondrial respiration may limit carbon assimilation rates in C3 plants at high temperatures (Braga et al. 2021).
Autotrophic and heterotrophic respiration have important roles in the impact of drought on the forest.Covariance tower estimates suggest that, in the dry season, there is a reduction in respiration in the forest in the Tapajós area (Restrepo-Coupe et al. 2017).The seasonality of the ED model for ecosystem respiration is almost exclusively driven by the seasonality of heterotrophic respiration, with a significant decline in the dry season, due to lower soil moisture (Powell et al. 2013).
Regarding GPP, the model algorithm would need a CO 2 absorption function based on field data to represent more accurately the forest dynamics in a scenario of increased atmospheric CO 2 .The values were close to the value of 25.6 Mg C ha -1 year -1 obtained for Tapajós by Restrepo-Coupe et al. (2013).Some studies suggest that there may be an acclimatization of species to CO 2 increase.Physiological processes often develop compensatory mechanisms that reduce or minimize the long-term effects of CO 2 (Dorneles et al. 2019).Acclimatization also may occur through the reduction of the maximum apparent rate of carboxylation (Ainsworth and Long 2021).An experiment with grasses suggested that the response to atmospheric CO 2 enrichment depends on the plant characteristics and environmental conditions, such as patterns of water use and acquisition of nutrients, which may be the key to understanding changes in plant communities (Morgan et al. 2004).Although there are several experiments worldwide to evaluate the effect of higher atmospheric CO 2 on forests (Norby et al. 2005;Karnosky and Pregitzer 2006), there are still no long-term results for tropical forests regarding the behavior of carbon absorption.
As already mentioned, the photosynthesis in the ED2.2 model is controlled by the equations of Farquar (1980) and Leuning (1995).Leuning's equation indicates that, when moisture deficit increases, gs decreases.However, if there is an increase in environmental CO 2 , gs decreases more sharply in this equation than in other equations, such as that of Ball and Berry (1987).Other ecosystem models that use the Ball and Berry equation do not consider the CO 2 compensation term, simulating lower gs values relative to the Leuning equation when there is high atmospheric CO 2 and low soil moisture.There are still no field data showing the combined effect of drought and increased CO 2 on tropical forests, therefore it is not yet possible to confirm whether the modelled results for the RCP4.5 and RCP8.5 scenarios are plausible.One of the main effects of the increase in CO 2 on plant carbon metabolism is the decrease in stomatal conductance (Leakey et al. 2009), although there is still no consensus on this subject.
A higher proportion of CO 2 in the atmosphere potentially increases photosynthetic activity, decreasing photorespiration and the Rubisco oxygenase activity (Buckeridge 2007).Another effect of increased atmospheric CO 2 is the increase in water use ratio between assimilated CO 2 and water loss.In our simulations, for RCP4.5 and 8.5, the water use efficiency increased by 24% in RCP4.5 and 31% in RCP8.5 relative to the control scenario.Possibly, biochemical damage occurred during leaf temperature increase due to the increase in ambient temperature, breaking or denaturing the enzymes involved in CO 2 fixation, causing photoinhibition or photodestruction (Roden et al. 1996).This result shows that, in a scenario with a high concentration of CO 2 , there may be a limitation in the increase of carbon in the forest biomass, since the higher value of atmospheric CO 2 in the scenario RCP8.5 resulted in a lower GPP in relation to RCP4.5.The high levels of CO 2 in the atmosphere can, according to the GPP equation, contribute to the increase in forest biomass.In the GPP calculation, the CO 2 assimilation rate can implicitly ignore the limitation of low soil moisture conditions, causing vegetation to continue absorbing carbon beyond what would be expected for a drought condition.Plant respiration can increase exponentially with increasing temperature, however, photosynthetic rates are known to increase until they reach the ideal temperature and then decrease (Fitter 1981).For example, the photosynthetic activity of Pistacia lentiscus in the field was high when the temperature was below 30° C, and decreased above this limit, showing that the increase in ACTA AMAZONICA temperature influences the assimilation of CO 2 (Gatti et al. 2010).
An important consequence of the effect of increased atmospheric CO 2 on plant physiology is a decrease of rainfall in the Amazon.Simulations with the Brazilian Atmospheric Model (BAM) from CPTEC/INPE estimated that the impact of plant physiology on the amount of rain in the forest is greater than the effect of deforestation, through the reduction in canopy transpiration as a function of decreasing stomatal conductance driven by the increase in atmospheric CO 2 (Sampaio et al. 2021).

CONCLUSIONS
The majority of processes in the ED2.2 model, including photosynthesis, depend on soil moisture.Our results showed that the precipitation reduction in RCP4.5 and RCP8.5 scenario conditions can directly impact soil moisture, and thus can cause a cascade effect leading to the increase of matrix potential and reduction of stomatal conductance, thus transpiration and GPP, indicating that a drier and warmer climate may limit the plant growth.The variability in the availability of water can affect the rate of tree growth, as the precipitation is the principal source of soil moisture and consequently water for the vegetation.However, there is an important point to be considered in a scenario with warmer temperature and deficient rainfall.Does the increase in CO 2 concentration contribute to increase primary net production, as shown in our results?This is an important result from the projections, because an atmosphere enriched with CO 2 can promote changes in the metabolism and other physiological processes of the trees.This area needs further investigations.It is still not clear how the physiology of the tropical vegetation reacts when CO 2 concentration attains higher values along with changes in the rainfall and temperature patterns.The use of the field data combined with the simulations with robust models like ED2.2 can help answer how the stomatal conductance, the principal process involved in the accumulation of biomass, can be affected.
photosynthesis if the stomata are closed;= photosynthesis if the stomata are open, breathing in the dark.
[4]    where M and D o are empirical constants and b is the cuticular conductance.Ds represents the water vapor deficit

Figure 1 .
Figure 1.Simplified illustration of the multiple hierarchical levels in the ED2.2 ecosystem demography model, organized by static levels (grid, polygons and sites) and dynamic levels (patches and cohorts).Adapted from Longo et al. (2019).
is the weighting for open stomata, A o and Ac stand for photosynthesis for open stomata and for closed stomata, respectively.A net and are considered to be linearly related under conditions of open stomata ( ) and closed stomata ( ), weighted by the plant's water availability (supply) relative to its total water demand.The weight that determines when the stomata are open ( amount of water accessible to the vegetation layer; broot = the vegetation layer's total C in fine roots; and = constant.

Figure 2 .
Figure 2. Monthly rainfall (A) and mean monthly volumetric soil moisture (m 3 m -3 ) interpolated for an 8-m soil profile in Tapajós National Forest for the interval from January 2002 to December 2004, according to field data (B) and model data (C).This figure is in color in the electronic version.

Figure 3 .
Figure 3. Average monthly volumetric values of soil water (m 3 m -3 ) interpolated for eight layers of an 8-m soil profile in Tapajós National Forest for the control scenario (A), and the RCP4.5 (B) and RCP8.5 (C) climate-change scenarios.Data for the period January 2002 to December 2010.This figure is in color in the electronic version.

Figure 4 .
Figure 4. Average hourly diurnal variation (6 am -18 pm) of vegetation productivity and physiological parameters in Tapajos National Forest over the period of January 2002 to December 2010 for a control scenario and two climate-change scenarios.A -gross primary productivity (GPP); B -stomatal conductance (gs); C -leaf temperature (t_leaf ); D -vapor pressure deficit (VPD).Plain lines represent the dry period and lines with triangles the rainy season.This figure is in color in the electronic version.

Table 3 .
Monthly energy balance components in the dry and rainy season for a control and two climate-change scenarios (RCP4.5 and RCP8.5) simulated for a nine-year period(2002 -2010)in the Tapajós National Forest.Average value for the dry and rainy season.LE = latent heat flux; H = sensible heat flux (W m -2 ).Values are the mean ± standard deviation.