During the last three decades, intensive campaigns and experiments have been conducted for acquiring micrometeorological data in the Amazonian ecosystems, which has increased our understanding of the variation, especially seasonally, of the total energy available for the atmospheric heating process by the surface, evapotranspiration and carbon exchanges. However, the measurements obtained by such experiments generally cover small areas and are not representative of the spatial variability of these processes. This chapter aims to discuss several algorithms developed to estimate surface energy and carbon fluxes combining satellite data and micrometeorological observations, highlighting the potentialities and limitations of such models for applications in the Amazon region. We show that the use of these models presents an important role in understanding the spatial and temporal patterns of biophysical surface parameters in a region where most of the information is local. Data generated may be used as inputs in earth system surface models allowing the evaluation of the impact, both in regional as well as global scales, caused by land-use and land-cover changes.
- surface energy budget
- CO2 fluxes
- eddy covariance
- remote sensing
- Amazon region
Amazon rainforests directly influences the terrestrial climate system due to the emission or absorption of carbon dioxide (CO2) and evapotranspiration (ET), that is, through the processes of transpiration of plants and evaporation of water contained in leaves, stems, litter and soil [1, 2]. In addition to providing water vapor to the environment, influencing the general circulation in the tropics and contributing to regional precipitation, the Amazon rainforests are important in the atmospheric carbon cycle [3, 4]. Consequently, deforestation in the Amazon can lead to changes in surface net radiation (Rn), resulting in higher or lower availability of energy for the evapotranspiration processes and in the amount of CO2 absorbed or released by the atmosphere [5, 6, 7].
The relevance of physical phenomena related to energy exchanges between the surface and atmosphere under climate change leads to the need for improving studies on both temporal as well as spatial scales [8, 9]. During the last three decades, intensive campaigns and experiments have been developed for acquiring micrometeorological data in the Amazonian ecosystems, which has increased our understanding of the variations, especially seasonally, of the total energy available for the atmospheric heating process by the surface, ET and atmospheric CO2 exchanges [10, 11]. However, measurements obtained by such experiments are usually local and representative of small areas, and therefore not representative of the spatial variability of these processes [12, 13].
In this context, new methodologies have been developed to obtain the components related to energy and CO2 exchanges between the surface and atmosphere, such as the use of remote sensing (RS). Usually, the use of orbital sensors to estimate energy and CO2 fluxes are performed using models that consider information obtained directly from the satellite images as inputs, such as reflectance and land surface temperature (LST) [14, 15]. Regarding the estimation of surface energy fluxes, several algorithms have been developed, such as the Simplified Surface Energy Balance Index (S-SEBI)  and Evapotranspiration Assessment from Space (EVASPA) . To estimate CO2 fluxes, we can highlight Parametric Production Efficiency Model (C-Fix)  and Temperature and Greenness Rectangle Model (TGR) . These models were applied in different terrestrial biomes; however, it is worth mentioning that in the Amazon region such approach for the determination of energy and CO2 fluxes using RS data is still incipient [20, 21, 22, 23, 24, 25].
Based on the considerations above, this chapter aims to present and discuss several models developed to estimate surface energy and CO2 fluxes by combining satellite data and micrometeorological observations, highlighting the potentialities and limitations of such models for applications in the Amazon region.
2. Biosphere-atmosphere interactions studies in the Amazon region using in-situ measurements
Since the 1980s, a series of micrometeorological experiments have been conducted in the Amazon region aiming to better understand the interactions between the rainforests and the atmosphere (i.e. Amazonian Research Micrometeorological Experiment (ARME, 1983–1985) , Amazonian Boundary-Layer Experiment (ABLE, 1985–1987) , Anglo-Brazilian Amazonian Climate Observational Study (ABRACOS, 1991–1995) , and Green Ocean Amazon Experiment (GO-AMAZON, 2014–2015) ). Currently, the main source of surface measurements in the region is the Large-Scale Biosphere-Atmosphere Experiment in Amazonia (LBA) . LBA has sites on different land-use locations in the states of Rondonia (RO), Amazonas (AM), Para (PA) and Tocantins (TO). LBA data have been used to analyze the current state of the Amazonian ecosystem, as well as to serve as input and validation parameters for climate prediction numerical models .
Typical variables collected at these surface experiments are incoming solar radiation (K↓), outgoing solar radiation (K↑), albedo (αs) [32, 33], incoming (L↓) thermal infrared (TIR) radiation, emitted TIR (L↑), net radiation (Rn) [34, 35], soil heat flux (G), sensible heat flux (H), latent heat flux (λE) [10, 36], and the net ecosystem exchange (NEE) [5, 37]. It is important to mention that most of the observational studies in the Amazon region have been performed over primary forest and pasture areas. In this context, one way to extend such analyses to the diverse ecosystems of the Amazon is the combined use of surface measurements (i.e. plot-level and flux towers biometric studies) and RS data [38, 39].
3. Modeling energy and CO2 fluxes combining remote sensing and ground data
The frequency at which satellite data are obtained and processed, combined with the possibility of regional and global studies, provides an excellent cost-benefit ratio. In recent years, there has been a gradual advance in the technical characteristics of the sensors onboard orbital platforms, which present increasingly improved spatial, temporal, radiometric, and spectral resolutions. Within this context, the scientific community has used orbital data to estimate surface biophysical and hydrological parameters using different algorithms. Focusing on the estimation of energy and CO2 fluxes using RS and ground observations, this topic presents the main models available in the literature that can be applied in the Amazon region.
3.1. Models to estimate energy fluxes
First studies to estimate energy fluxes using RS date back to the 1970s , driven by the limited spatial density of surface measurements, which prevented more robust large-scale studies . Currently, studies are focused not only in the estimation but also on describing the land-vegetation-atmosphere energy exchange processes in order to better understand, for example, the feedback mechanisms between the surface and the boundary layer. This issue is gaining importance due to potential climate change .
Energy fluxes models differ according to the input data, assumptions and accuracy of the results [43, 44]. However, a common aspect among the algorithms is the orbital input data, once all algorithms require information regarding the visible, near infrared and thermal infrared spectral regions. The primary estimates from such models are related to Rn, G, H, λE and, consequently, ET. ET is considered a key variable in such models, and, likewise, the most complex variable when referring to the accurate estimate. Figure 1  exemplifies ET estimates in the Amazon region obtained through MODIS images. Briefly, according to Ruhoff et al. , such algorithms are based on (1) empirical and statistical methods, (2) residual energy balance methods, and (3) other physical methods (i.e. Penmann-Monteith equation ).
3.1.1. Surface energy balance algorithms for land (SEBAL)
SEBAL  is a model based on empirical relationships and physical parametrizations. It was developed to estimate the energy available at surface using daily orbital data and minimal field measurements. Input variables are related to air temperature and wind speed during the satellite passing. SEBAL has been improved since its conception, for example, with the addition of new parametrizations such as those for αs , and G .
The algorithm consists of several steps, with Rn being the first component of the energy balance to be obtained. Following Rn, it is possible to estimate G (as a function of Rn, normalized difference vegetation index (NDVI), αs, and land surface temperature (LST)), and H, which requires the determination of pixels representing extreme conditions of temperature and humidity in the study area, referred to as hot and cold pixels. The determination of hot and cold pixels is an issue, where the lack of user-experience can introduce errors, such as defining fire pixels as hot pixels and cloud pixels as cold pixels . Recent studies proposed statistical approaches to automatically select hot and cold pixels . One of the last steps of SEBAL is the estimation of daily actual ET (ETr24h):
where ᴧ is the evaporative fraction, Rn24h is the average daily radiation budget, and λ corresponds to the latent heat of water vaporization (λ = 2.45 × 106 J Kg−1).
SEBAL has been applied and validated in different regions [14, 52, 53, 54]. This model is sensitive to land-use, allowing for evaluations in agricultural areas, deserts, prairies, and forests [55, 56]. Regarding the accuracy of the estimates, studies indicate relative errors ranging between ~5 and 17% [14, 57, 58, 59]. The error variation was mostly related to the spatial resolution of the satellite images used. Also, it should be highlighted that the main sources of uncertainties in SEBAL are related to the determination of H and the low sensitivity of the model to soil moisture and water stress .
Studies using SEBAL have been conducted in the Amazon region, such as in De Oliveira and Moraes , De Oliveira et al. , Liberato et al. , Santos et al. , and Ferreira et al. . These studies were performed in the southwestern and eastern parts of the Amazon using LBA data from the following sites: Fazenda Nossa Senhora Aparecida (FNSA) (RO), Reserva Biologica do Jaru (RBJ) (RO), Floresta Nacional de Caxiuana (CAX) (PA), and Floresta Nacional do Tapajos (FNT) (PA). Orbital input data were acquired from the Moderate Resolution Imaging Spectroradiometer (MODIS) sensors onboard Terra and Aqua satellites and the Thematic Mapper (TM) sensor onboard LANDSAT-5. Results found for Rn were satisfactory, presenting relative errors of ~1–16%. For ET, the errors were higher, in the order of ~25%. It should be noted that such studies were conducted over relatively small/medium areas (~7500.000 hectares) and some of them covered only pixels where the flux towers were located due to the difficulty in acquiring cloud free images.
A possible way to operationalize SEBAL for larger scale studies in the Amazon region is using data from 8 or 16 days composites or monthly images from MODIS sensor , in which cloud cover effects are attenuated. Although considering that the algorithm was developed for daily images, difficulties emerge related to the surface input data, which need to be acquired during the satellite crossing. In this regard, we highlight the study conducted by De Oliveira et al. , in which an approach was developed to estimate Rn and its components under all-sky conditions for the Amazon region through SEBAL model utilizing only RS and reanalysis data. Comparison between estimates obtained by the proposed method and observations from LBA towers showed errors between ~13–16% and ~11–16% for instantaneous and daily Rn, respectively. According the authors, the approach was an alternative to minimize the problem related to strong cloudiness over the region and allowed for consistently mapping the spatial distribution of net radiation components in Amazonia. In this regard, we highlight that further studies should focus in the determination of ET, the most important component of the Amazon hydrological balance.
3.1.2. Simplified surface energy balance index (S-SEBI)
S-SEBI  is a semi-empirical model developed soon after SEBAL, such that both models are very similar. The main differences between both models are related to the estimation of thermal infrared radiation emitted from the surface, H and λE , which will be discussed further. S-SEBI needs spectral radiance orbital data obtained during clear sky conditions from visible, near infrared and thermal infrared spectral regions to define the initial variables of the model, which are the reflectance, LST and vegetation indices. From these initial variables and the inclusion of air temperature data, it is possible to estimate all the energy balance terms [65, 66].
Rn is estimated from the residual term of solar radiation and thermal infrared exchanges, and G is estimated from the empirical relationship between the characteristics of the surface and the vegetation . It is important to highlight that G is one of the components of the energy balance equation most difficult to be accurately estimated using RS data. Therefore, regardless of the parametrization or the model applied, the equation to obtain G must be adjusted locally in order to achieve better results . It is important to mention here that in forested areas such variable is not relevant to the energy balance; however, over bare soil or areas with sparse vegetation G is an important component of the energy balance.
H and λE are estimated from the evaporative fraction (∋) , consisting on the main difference between SEBAL and S-SEBI models . In S-SEBI, sensible and latent heat fluxes are obtained at the same time directly from the ᴧ, while in SEBAL such variables are estimated separately. Thus, it is not necessary to select pixels representing the null conditions of the fluxes when using S-SEBI. According to Roerink et al. , there is a correlation between reflectance and LST in areas presenting constant atmospheric forcings. Therefore, it is assumed that the ᴧ varies linearly with LST for a given albedo. By using regressions, it is possible to identify the superior (drier, higher H) and inferior (wetter, higher λE) limits of LST. From the instantaneous values of H and λE, daily ET can be estimated for the entire image.
Studies based on S-SEBI generally use TM/LANDSAT-5 data and are focused on evaluating agricultural areas in Europe and Asia [69, 70, 71]. In Brazil, S-SEBI was applied in the semi-arid  and in the southwestern regions . Errors found in these studies ranged from ~10 to 30%. It is worth mentioning that S-SEBI usually presents higher errors than those obtained from SEBAL, which, according to Sobrino et al. , is related to the more robust estimation of H in the algorithm proposed by Bastiaanssen et al. . However, there are advantages when using S-SEBI, such as the need of only one surface variable input (air temperature). In this case, the choice of the algorithm depends on both the availability of surface data and the intended application. In relation to Amazonia, a region with a lack of surface observations, S-SEBI may be a suitable proposition. Nevertheless, such as pointed out for SEBAL, the ideal application of S-SEBI in the region should focus on the use of MODIS composites.
3.1.3. Surface energy balance system (SEBS)
SEBS  is a single-source model developed to estimate the atmospheric turbulent fluxes using RS data. In single-source models, which also include SEBAL (Section 3.1.1) and S-SEBI (Section 3.1.2), the general assumption made is that the radiometric surface temperature measured by a radiometer (orbital sensor) is equivalent to aerodynamic surface temperature . As discussed in the previous sections, these models are based on the difference between dry and wet limits to estimate ET on a pixel-by-pixel basis. Such limits usually follow these characteristics: (1) maximum (minimum) LST, and (2) low or no (high or maximum) ET .
To generate such estimates, SEBS requires three types of input datasets. The first dataset consists on αs, LST, vegetal cover fraction, and leaf area index (LAI) which usually obtained from RS images combined with specific information of the study area [76, 77]. Additional data includes vapor pressure deficit, air temperature and humidity, as well as wind speed, obtained from surface-level stations or reanalysis data. The third dataset is related to the incoming solar and thermal infrared radiation fluxes, which can be obtained directly from the surface-level measurements or reanalysis data.
Estimates of Rn and G follow the same assumptions as SEBAL and S-SEBI, while the estimates of H and λE present differences. In SEBS, for the dry limit, λE is assumed as zero (λEdry), due to the soil moisture limitation, meaning that H reaches its maximum value (Hdry). Considering the wet limit, ET occurs in the potential rate (λEwet), and H reaches its maximum value (Hwet). After the calculation of Hdry, Hwet and H, based on Monin-Obukhov Similarity Theory , the relative evaporation and reference evaporation fractions (ᴧr and ᴧref, respectively) are obtained from Eqs. (2) and (3).
By inverting Eq. (3), it is possible to determinate λE for all pixels of the image. It is worth mentioning that during the parametrization of the turbulent processes in the layer immediately above the vegetation is necessary to define the surface roughness length . Most of the algorithms consider a fixed value for the surface roughness length, while SEBS proposed a new formulation to define such variable, which, according to Li et al. , is one important advantage of using SEBS, since H is estimated more accurately.
Several studies have shown the potential of SEBS in daily, monthly and annually estimates of ET on local and regional scales [80, 81, 82, 83]. Among the studies presented above, we highlight the work developed by Jia et al.  to estimate ET in the delta of the Yellow river in China. The authors used MODIS composites of reflectance, LST, and LAI to obtain ET values for 14 different land-use types, achieving mean square errors of ~0.9–1.3 mm. Overall, studies show that the errors between SEBS estimates and in situ measurements range between ~8 and 15% [84, 85]. Summarizing, SEBS presents advantages when compared to other algorithms, such as the surface roughness length estimate and the possibility of using MODIS composites; however, it requires a large number of surface parameters, which in regions like the Amazon can be an important issue.
3.1.4. Evapotranspiration assessment from space (EVASPA)
EVASPA  is a model developed to estimate ET using RS data considering spatial and temporal scales relevant for hydrological studies. Important characteristics of this algorithm include: (1) possibility of integrating data from multi-sensors, (2) estimation of the uncertainties, and (3) production of ET maps for days when there are no RS images available. EVASPA is based on S-SEBI  (Section 3.1.2) and the triangle method , which are very similar in general. The study of Gillies et al.  provides a review of the principles of the triangle method to estimate ET.
EVASPA model is focused on generate ET estimates on the kilometric scale using MODIS sensor data from both Terra and Aqua satellites. However, the algorithm enables the generation of estimates using higher spatial resolution sensors, such as TM/LANDSAT 5 and ASTER/Terra. In this regard, we highlight that this is a relatively recent model where equations for higher spatial resolution sensors are still not implemented. EVASPA estimates are generated using MODIS daily and eight- or 16-day data regarding αs, LST, emissivity, LAI, and vegetation indices. The surface-level input data required consist in incoming solar and thermal infrared radiation. Numerical terrain information is also necessary and is usually obtained from the global digital elevation model GTOPO30 (http://edcdaac.usgs.gov/gtopo30/gtopo30.asp).
The model has several equations for each parameter necessary to estimate ET, such as Rn , G , and ᴧ . Therefore, different estimates of ET are provided depending on the input data, enabling the evaluation of the uncertainties in the estimates of ET. Still, the model contains algorithms to interpolate ET estimates in days without orbital data or cloud cover . Consequently, the model is an interesting option for applications in the Amazon, where it is difficult to obtain cloud free data in the region. Finally, it is worth mentioning the possibility of comparing EVASPA estimates with MODIS global ET product (MOD16) , which will be discussed in sequence. EVASPA generates as outputs graphics of accumulated monthly and annual ET, difference maps, and dispersion diagrams.
Initially, EVASPA validation was performed using in situ data acquired from a site located in southern France between 2009 and 2011 . Mean square error corresponded to 0.78 mm, while R2 was 0.76. It is noteworthy that both the characteristics of the model (i.e. reduced surface data required and the possibility of estimates for days without RS images available) and initial validation results are promising, therefore EVASPA presents a considerable potential for application in the Amazon region.
3.2. Models to estimate CO2 fluxes
The eddy covariance system is the most common way to evaluate the carbon balance over terrestrial ecosystems . However, estimates obtained from such system represent only fluxes at the tower scale, which ranges from hundreds of meters to a few kilometers. Therefore, many studies have been conducted aiming to understand the processes involving the carbon gained from ecosystems through photosynthesis and the carbon loss through respiration using RS data and modeling .
Most of the models are based on a radiation use efficiency (RUE) approach, although there are other empirical approaches. The concept of RUE was proposed by Monteith  and later became the basis for the use of RS to quantify the vegetation productivity. The algorithms are based on the relationship between RUE, absorbed photosynthetically active radiation (APAR), fraction of absorbed photosynthetically active radiation (fAPAR), and additional environmental variables that may limit photosynthesis . Major difficulties in estimating RUE at large areas include dependency of environmental variables and the vegetation characteristics, as well as issues to estimating APAR (i.e. dependency of atmosphere dynamics) . The primary outputs of these models are related to gross primary productivity (GPP), net primary productivity (NPP), ecosystem respiration (Reco), and net ecosystem carbon exchange (NEE). Figure 2  illustrates GPP estimates in the Amazon region using MODIS images.
3.2.1. Carnegie-Ames-Stanford approach (CASA)
CASA  is a model based on the processes of carbon assimilation and respiration to estimate NPP using satellite observations. The model incorporates assumptions of most biogeochemical algorithms, that is, CO2 fluxes are controlled by ecosystem properties and driven by climate variability. The CASA formulation is based on the concept of vegetation greenness [96, 97]. Vegetation greenness level can be estimated from vegetation indices derived from RS, e.g. NDVI, given the good correlation between these indices with different biophysical parameters of the vegetation (i.e. fAPAR, LAI) .
CASA estimates NPP from RUE . Thus, plant biomass production is estimated as a product of incoming solar radiation (K↓), fAPAR, and a term of radiation use efficiency (ε) (ε = 0.389 g C m−2 MJ−1), which is multiplied by scale factors (f) of air temperature (Tair) and soil moisture (w), according to Eq. (4):
As noted, air temperature and soil moisture are used to reduce the RUE from the maximum value. CASA requires surface measurements related to solar radiation, air temperature and precipitation as input data. The estimates generated from the model are usually well correlated with NPP obtained from the regional scale field observations; however, when compared to specific ecosystems (i.e. agricultural crops, forests and pastures) the correlations are low . According to Yu et al. , this occurs because maximum RUE from CASA (ε = 0.389 g C m−2 MJ−1) is not comparable to the RUE from diverse biomes.
3.2.2. Parametric production efficiency model (C-Fix)
C-Fix  is a model based on Monteith  and developed to quantify carbon fluxes on local, regional and global scales [101, 102]. Similar to CASA (Section 3.2.1), the key-element of C-Fix is that the biophysical state of the vegetation cover can be inferred from RS data. Therefore, C-Fix is basically derived from three steps: (1) mapping the vigor of the vegetation using NDVI estimated from orbital sensors, (2) estimation of fAPAR based on the relationship proposed by Myneni and Williams , and (3) inclusion of air temperature and incoming solar radiation measurements.
C-Fix provides the estimation of GPP, NPP, and net ecosystem productivity (NEP) according to the following equations:
In Eqs. (5)–(7), f(Tair) is a normalized factor of air temperature, f(CO2,fert) is a normalized factor of CO2 fertilization, ε is the term of radiation use efficiency (ε = 1.10 g C m−2 MJ−1), c is the climatic efficiency (c = 0.48) , Ra is the autotropic respiration, and Rh is the heterotrophic respiration. Variables Ra and Rh are obtained from the algorithms proposed by Veroustraete et al. . Maximum RUE in C-Fix is constant (ε = 1.10 g C m−2 MJ−1), reduced by the normalizing factors of air temperature and fertilization by CO2 dependency. Meteorological input data for the model are incoming solar radiation and air temperature.
Regarding C-Fix validation, studies indicate a reasonable correlation between fluxes estimated from the model and eddy covariance measurements (R2~0.75) . Recent upgrades in C-Fix, such as the insertion of hydric limitation functions have provided an improvement in the model performance when compared to field measurements . However, there is a lack of studies to precisely evaluate the main sources of uncertainties in the model.
Studies conducted in Europe, using orbital data derived from AVHRR/NOAA and VEGETATION/SPOT 4 [18, 107], show that the model provided a solid basis for estimating the temporal and spatial distribution of the main components of the carbon budget in forest ecosystems on a regional scale. Such results, combined with the performance assessment and the requirement of few in situ information, show the potential of applying C-Fix in Amazonia.
3.2.3. Vegetation photosynthesis model (VPM)
VPM  was developed to estimate GPP in forest areas using vegetation indices obtained from optical sensors. During the last three decades, NDVI time series have been used in modeling GPP and NPP ; however, NDVI presents limitations, such as the sensitivity to atmospheric aerosols . The inclusion of spectral bands located in the blue and short wave infrared regions in sensors such as the VEGETATION/SPOT 4 and MODIS/Terra and Aqua enabled the estimation of different vegetation indices that reduced some of the limitations and uncertainties imposed when merely using NDVI. In view of that, estimates generated from VPM consider EVI  and the land surface water index (LSWI) .
VPM is also based on an RUE approach, however it presents a key difference which is assuming that forest canopy is composed of photosynthetically active vegetation (PAV) (i.e. chloroplasts) and non-photosynthetically vegetation (NPV) (i.e. senescent leaves and branches) . GPP estimated using VPM is obtained from the following equation:
In Eq. (8), fAPARPAV is the fraction of photosynthetically active radiation absorbed by PAV, and IPAR represents the incoming photosynthetically active radiation. fAPARPAV is estimated as a linear function of EVI . The contribution of fAPAR in fAPARPAV and fAPARNPV is important, since the presence of NPV significantly affects fAPAR at the canopy scale. For example, in forests with LAI < 3.0, NPV increased fAPAR by ~10–40% . Also, it is important to point out that only fAPARPAV is used in photosynthesis. Therefore, it is evident that this partition is a critical issue when modeling GPP or NPP in forests, considering fAPARPAV may substantially increase the estimates. However, most of the CO2 fluxes algorithms do not incorporate this assumption.
Another highlight of VPM is that the term ε is not constant, as opposed to CASA and C-Fix, varying according to the vegetation. ε parametrization in distinct forest formations is given by NEE and IPAR measurements obtained from flux towers located in specific sites. Research was conducted to define this variable in the boreal forest (ε = 2.21 g C m−2 MJ−1) , and also in tropical rainforest (ε = 2.48 g C m−2 MJ−1) . Functions of air temperature, phenology, and water content of leaves (estimated from LSWI) are used to reduce the scale of ε. Required surface information of VPM are air temperature, NEE and IPAR.
Regarding the validation of VPM, Liu et al.  obtained R2~0.88 when comparing the model outputs with surface measurements, while Jiang et al.  found relative errors of ~59%. According to Xiao et al. , the main sources of errors of VPM are related to the low sensitivity to PAR and air temperature, as well as the non-correction of the bidirectional effects on vegetation indices. VPM was applied to different forest ecosystems across the globe, among them, the Amazon rainforest . The study conducted by Xiao et al.  used VEGETATION/SPOT 4 and MODIS/Terra and Aqua (daily and 8-day composites) data to generate estimates of GPP over the FNT/K67 site in the state of Para, Brazil. The model estimates showed high NPP in the end of the dry season, which was consistent with the high ET and GPP measured by the micrometeorological tower.
VPM presents a high potential for the seasonal estimation of productivity in tropical forests. However, most of the studies using the model generated estimates only for the tower pixel and adjacent areas (i.e. 3x3 pixels) [114, 115]. Despite the possibility to retrieve GPP locally with a reasonable accuracy , the operationalization of VPM for regional analyzes requires modifications to the model, mainly related to the estimation of e for distinct forest formations and/or large areas.
3.2.4. Temperature and greenness rectangle model (TGR)
TGR  was developed to estimate the productivity of terrestrial ecosystems using MODIS/Terra and Aqua data. The model is based on studies conducted by Rahman et al. , in which a strong linear correlation between EVI and GPP in different forest formations was shown, and Sims et al. , which showed that LST can be used to infer the influence of water stress on GPP. Thus, TGR uses as inputs EVI and LST derived from MODIS and in situ IPAR measurements to estimate GPP on 16-day intervals. Three major aspects of TGR should be highlighted: (1) the algorithm strictly follows the RUE concept, (2) it has a low dependency of surface measurements, and (3) the overlapping of information in correlated explanatory variables is avoided.
The term ε* refers to the amount of carbon fixed per unit of IPAR. It should be noted that this assumption is different from the traditional definition of RUE, which is the amount of carbon fixed per unit of APAR. In TGR, as well as in most of the vegetation productivity models, the term of radiation use efficiency is multiplied by a scale factor, aiming to reduce estimates under unfavorable conditions (i.e. high or low temperature and high vapor pressure deficit). For this purpose, EVI  and LST  are used. According to Yang et al. , it is inappropriate to simply multiply the effect of these two variables, considering that both are physically interdependent. Therefore, to define the f value from EVI and LST the algorithm proposes a methodology based on the least square method . Studies indicate that IPAR may range from ~40 to 50% of the incoming solar radiation . Thus, Yang et al.  suggest the use of in situ measurements of this variable in order to reduce the uncertainties.
In TGR, as for VPM (Section 3.2.3), the term RUE is not constant, allowing the calibration for different vegetation formulations. The study of Yang et al.  described values of this term for eight types of vegetation, including pasture, savanna, and mixed forest. This study also validated the model considering measurements obtained from 13 different experimental sites in the United States. Results showed that estimates from TGR agreed with tower flux measurements for almost all types of vegetation, with R2~0.67–0.91. TGR allows to capture the GPP patterns over large areas, which is necessary for applications in the Amazon region. In this context, we highlight that the use of IPAR data obtained directly from MODIS  would eliminate the need of in situ measurements, enhancing the potential of TGR for applications in Amazonia. According to Yang et al. , future studies will focus on validating TGR estimates over tropical forest areas.
3.3. Remote sensing global products
RS is the main tool for observing the state and processes of terrestrial surface and atmosphere . LANDSAT, SPOT, NOAA, Terra and Aqua platforms have provided time series of data in different spatial and temporal resolutions, which are applied in a wide range of studies . One application is related to global climate change, where RS data have been used as inputs in climate models to simulate climate dynamics and future projections . Accordingly, it is notable an effort of the scientific community in generating RS derived standardized global products, specially related to the biophysical domain.
Currently, some of the most important global products based on satellite observations are derived from MODIS/Terra and Aqua sensors. MODIS was developed by the Goddard Space Flight Center (GSFC/NASA) and presents an imaging system composed by 36 spectral bands, from the visible to the thermal infrared regions. MODIS temporal resolution is daily for latitudes above 30° and 2 days for latitudes below 30° . Surface products derived from MODIS are related to αs , LST , vegetation indices , land-use  and other variables. More specifically, regarding energy and carbon fluxes, we highlight the ET (MOD16) , GPP and NPP (MOD17)  products.
The MOD16  product was developed to estimate global surface ET from MODIS/Terra and Aqua data and meteorological information obtained from the Global Modeling and Assimilation Office (GMAO). The algorithm is based on Penmann-Monteith equation :
In Eq. (10), Δ is the gradient of saturated vapor pressure to air temperature, Rn is the net radiation, G is the soil heat flux, ρa is the air density, cρ is the specific heat of air at constant pressure, es and ea are the saturated vapor pressure and actual vapor pressure, respectively, γ is the psychometric constant (0.066 kPa°C−1), and rs and ra are the surface and aerodynamic resistance, respectively. MODIS input data in the algorithm include αs, LAI, and land-use. Regarding the meteorological variables, solar radiation, air temperature, and water vapor pressure reanalysis data are used. Summarizing, MOD16 data are provided with spatial resolution of 500 m and 1 km and cover an area of ~109 millions of km2. MOD16 provides potential and actual ET fluxes at 8 days, monthly and annual intervals.
MOD16 was initially validated using measurements from 46 different tower fluxes across the United States, obtaining R2~0.65 . It is possible to point out main two sources of uncertainties related to MOD16: (1) GMAO reanalysis data, mostly due to the low spatial resolution (~100 km) when compared to MOD16 (500 m and 1 km), and (2) LAI and land-use products, which may present reasonable inaccuracies depending on the biome, which, consequently, will result in the incorrect determination of parameters to calculate plants transpiration . Most studies using MOD16 are focused on Asia and Middle East, aiming to evaluate watersheds [131, 132] and different land-uses, especially in agricultural areas . Validation performed on such studies agree with results found by Mu et al. .
Recent studies validated MOD16 in the Cerrado and Amazon biomes [45, 25]. Over Cerrado, the algorithm presented relative high correlation coefficients, ranging between ~0.78 and 0.81 . Results obtained for the Amazon were less satisfactory. Validation performed using tower fluxes data located over forest and pasture areas showed R2 values between ~0.32 and 0.76 . It should be noted that simplifications in MOD16 algorithm regarding some parameters such as canopy conductance are defined as constant for a given biome (even in a heterogeneous one, such as the Amazon). This may be one of the reasons for low correlations between the estimated and observed data in the region. This is actually one of the main challenges of global algorithms, which need to be complex to accurately represent the physical processes on the surface, and simultaneously simple enough to be implemented globally . Despite this, MOD16 was able to represent the spatial variability of ET in the Amazon. This is an important result and one interesting way to better evaluate the results of this model for the Amazon would be through the comparison between MOD16 outputs with more local estimates based on the models described in Sections 3.1.1–3.1.4.
The MOD17 product  provides continuous estimates of GPP and NPP over the vegetated surface of the planet. As well as models described in Sections 3.2.1–3.2.4, the MOD17 algorithm is based on the RUE approach . According to this approach, the productivity of vegetation under reasonable water and soil fertility conditions is linearly correlated with the amount of APAR. MOD17 is based on three basic relationships (Eqs. (11)–(13)) to estimate GPP and net photosynthesis (PSNet), on eight-day and monthly intervals, and annual NPP.
In the equations presented above, f(Tair,min) and f(VPD) are scale factors associated, respectively, to minimum air temperature and vapor pressure deficit, Rlr is the maintenance respiration of leaves and thin roots, Rg is the growing respiration, and Rm represents the maintenance respiration of living cells in the woody tissue. It is worth mentioning that the algorithm defines distinct values for ε, depending on the vegetation. ε values are distinct for forest, savanna, pasture, and agricultural areas. Tair,min and VPD values, as well as respiration values, are based on a lookup table composed of specific physiological parameters for each terrestrial biome . MOD17 product is estimated from MODIS standard products (i.e. fAPAR and LAI) and reanalysis data (i.e. air temperature and solar radiation) from the National Center for Environmental Prediction/National Center for Atmospheric Research (NCEP/NCAR). MOD17 outputs (GPP, PSNet (eight-day and monthly), and NPP (annual)), as well as MOD16 outputs, are provided with 500 m and 1 km spatial resolution.
Validation studies comparing MOD17 estimates with flux tower measurements found relative errors between ~24 and 70%, and correlation coefficients ranging between ~0.26 and 0.88 [135, 136, 137]. Generally, GPP and NPP derived from MOD17 follow the expected seasonal patterns according to the land-use and climate; however, values tend to be overestimated over low productivity sites (i.e. croplands), and underestimated over high productivity sites (i.e. forests). The main sources of errors in MOD17 are associated with the MODIS fAPAR product and reanalysis data .
MOD17 product has been validated over different regions [137, 139, 140]. Regarding the Amazon, an important area in the global carbon cycle, we highlight the study recently developed by De Oliveira et al.  in Para state, eastern Brazilian Amazonia. The mean relative error found for MOD17 GPP was about 13% of the field measurements (LBA flux towers). An underestimation was observed for primary and secondary forests (−4.1 and − 3.6 g C m−2, respectively) and an overestimation for pasture (2.2 g C m−2). According to the authors, the MOD17 product was able to provide reliable information about the spatial and temporal variability of GPP in the eastern flank of Amazonia.
4. Concluding remarks
Micrometeorological studies in Amazonian ecosystems have limited spatial and temporal coverage, and therefore RS becomes a tool to enhance the comprehension of surface processes in the region. Models to estimate energy and carbon balance components from orbital data differ according to the input data, parametrizations and accuracy of the results. The algorithms to estimate energy fluxes use as inputs images from visible and infrared (near and thermal) spectral regions and are based on empirical and physical methods. In situ measurements are typically related to air temperature and wind speed, and most uncertainties are concentrated in the estimation of H and ET (when obtained as a residual term of the energy budget). On the other hand, CO2 fluxes models need data from the visible and near infrared spectral regions and are based on the RUE concept. Main challenges of such models consist in the estimation of RUE for different ecosystems, as well as to obtain surface solar radiation data with a reasonable spatial resolution.
Regarding the use of such models in the Amazon region, some difficulties emerge: (1) obtaining cloud free orbital data, and (2) availability of field observations. Therefore, the choice of the algorithm must consider the possibility of using daily composites, and minimal need of in situ data. Other issues, such as the complexity and operability of the models may be considered. It is then possible to point out algorithms that present greater potential of application in the region and/or where efforts for implementation should focus. Regarding energy balance, two models stand out: SEBAL , due to the reduced need for field measurements and because the model was previously validated in the region and showed good results, and EVASPA , due to the operability and possibility of generating estimates during days when there are no orbital data available. In relation to the carbon models, it is suggested the use of VPM , once the model was applied to distinct forest ecosystems (including the Amazon) showing good results, and TGR , due to the fact that the model is based on MODIS composites and has a low dependence of field data.
Regarding the use of global RS products in the Amazon, it is important to emphasize that such products usually enable the analysis of spatial patterns of surface parameters; however, they present inaccuracies when referring to the magnitude of the estimates. A noteworthy aspect is that studies conducted in tropical regions, among them the Amazon, have proposed methodologies based on integrating satellite images and reanalysis climate data in hydrological and ecosystem models based on local measurements [2, 22, 23, 45, 141, 142]. Although there are difficulties, for example those related to representing the ecophysiological processes from leaf to canopy scale, such approaches constitute promising opportunities for future research.
The use of models based on satellite images presents an important role in understanding the spatial and temporal patterns of biophysical surface parameters in a region where most of the information is local. Data generated from such algorithms may be used as inputs in earth system surface models allowing, among others, to evaluate the impact, both in regional and global scales, caused by land-use and land-cover changes.
Gabriel de Oliveira acknowledges CNPq (Grant No. 52521/2012-7) and CAPES (Grant No. 8210/2014-4) agencies for providing research fellowships. Guilherme A. V. Mataveli acknowledges CNPq agency for a doctoral scholarship (Grant No. 162198/2015-0). Luiz E. O. C. Aragao acknowledges the financial support of FAPESP (Grant No. 50533-5) and CNPq (Grant No. 304425/2013-3) agencies.