The Inﬂuence of Land Surface Temperature in Evapotranspiration Estimated by the S-SEBI Model

: Evapotranspiration (ET) is one of the least understood components of the hydrological cycle. Its applications are varied, from agricultural, ecological and hydrological monitoring, to control of the evolution of climate change. The goal of this work was to analyze the inﬂuence that uncertainties in the estimate of land surface temperature (Ts) can cause on ET estimates by S-SEBI model in the Pampa biome area. Also, the speciﬁcities of native grassland of Pampa biome related to energy balance were analyzed. The results indicate that the daily evapotranspiration is higher when the pixel Ts is lower, which also shows the inﬂuence of land use on the variability of ET. The results demonstrated that the S-SEBI is less dependent on Ts estimation than other models reported in the literature, such as the SEBS, which not exceed 0.5 mm / day in grasslands. The evapotranspiration variability between forest and grassland were lower than expected, demonstrating that the Pampa biome have in Rio Grande do Sul the same importance that forests regarding to the processes of the hydrological cycle, since it covers 63% of the State.


Introduction
The physical, chemical and biological processes responsible for life on Earth depend practically on solar energy. Monitoring energy and soil-vegetation-atmosphere mass transfers is a key step in the management of water and agricultural resources, with different applications depending on the spatial and temporal scales of interest. It is also useful for a better understanding and prediction of climate evolution [1,2].
There are two ways of thinking about evapotranspiration: (1) hydrologically, in which ET is what is loss of water in the hydrological cycle by the plants; In this sense, precipitation, subsurface runoff, surface runoff, and evapotranspiration should also be taken into consideration [2]; (2) energetically, when considering the energy used for the process of water loss by the plants to the atmosphere by determining the magnitude of radioactive and non-radiative fluxes [1,3]. The radiation balance area of approximately 750,000 km 2 , shared by Brazil, Uruguay and Argentina. In Brazil, this biome is restricted to 63% of the State of Rio Grande do Sul (RS) and represents 2.07% of the national territory.
From the point of view of biodiversity and environmental services, the fields are a fodder source for cattle ranching, shelter diversity of plant and animal species, and ensure the conservation of water resources [22] The experimental site is located in the Federal University of Santa Maria (UFSM), covering 24 ha of natural vegetation (native grassland) belong to Pampa biome ( Figure 1). This study area is part of the International Long Term Ecological Research (ILTER) network and is used for experiments in several areas of knowledge, mainly focused on the morphology of native species for livestock production [23,24].
Atmosphere 2020, 11, x FOR PEER REVIEW 3 of 18 is restricted to 63% of the State of Rio Grande do Sul (RS) and represents 2.07% of the national territory.
From the point of view of biodiversity and environmental services, the fields are a fodder source for cattle ranching, shelter diversity of plant and animal species, and ensure the conservation of water resources [22] The experimental site is located in the Federal University of Santa Maria (UFSM), covering 24 ha of natural vegetation (native grassland) belong to Pampa biome ( Figure 1). This study area is part of the International Long Term Ecological Research (ILTER) network and is used for experiments in several areas of knowledge, mainly focused on the morphology of native species for livestock production [23,24].

Simplify Surface Energy Balance Index (S-SEBI)
The estimation of evapotranspiration from remote sensing data uses thermal infrared (TIR) sensors on satellite, which is based on assessing the energy balance through several surface properties such as albedo, vegetation cover and surface temperature [3]. When considering instantaneous conditions, the surface energy balance is obtained by determining the magnitude of the radiative and non-radiative fluxes the energy balance is written as: where LE is the latent heat flux of evaporation or evapotranspiration due to ET; Rn is the surface net radiation; H is the sensible heat flux; and G is the soil heat flux. The variables are expressed in energy units (W/m 2 ). ET in volume units (e.g., liters m −2 d −1 , usually simplified to mm d −1 to express ET as a depth of water over an indefinite area) can be calculated from LE by the amount of energy needed to evaporate water at a specific temperature and pressure 62 .
Once the surface energy balance equation is discriminated, the Rn is calculated as the rest term of all incoming and outgoing shortwave (sw) and longwave (lw) radiation, as describing below: Rn = (1 − α)Rs ↓ + εRL ↓ − εσTs (2) where Rs (W/m 2 ) is the shortwave downward radiation; RL (W/m 2 ) is the longwave downward radiation; α is the surface albedo; ε is the surface emissivity; Ts (K) is the land surface temperature and σ is the Steffan-Boltzmann constant (5.67 × 10 −8 W m −2 K −4 ). The latent heat flux (LET) depends on the evaporative fraction (Λ) and is given as follows:

Simplify Surface Energy Balance Index (S-SEBI)
The estimation of evapotranspiration from remote sensing data uses thermal infrared (TIR) sensors on satellite, which is based on assessing the energy balance through several surface properties such as albedo, vegetation cover and surface temperature [3]. When considering instantaneous conditions, the surface energy balance is obtained by determining the magnitude of the radiative and non-radiative fluxes the energy balance is written as: where LE is the latent heat flux of evaporation or evapotranspiration due to ET; Rn is the surface net radiation; H is the sensible heat flux; and G is the soil heat flux. The variables are expressed in energy units (W/m 2 ). ET in volume units (e.g., liters m −2 d −1 , usually simplified to mm d −1 to express ET as a depth of water over an indefinite area) can be calculated from LE by the amount of energy needed to evaporate water at a specific temperature and pressure 62 .
Once the surface energy balance equation is discriminated, the Rn is calculated as the rest term of all incoming and outgoing shortwave (sw) and longwave (lw) radiation, as describing below: Atmosphere 2020, 11, 1059 4 of 18 where Rs (W/m 2 ) is the shortwave downward radiation; RL (W/m 2 ) is the longwave downward radiation; α is the surface albedo; ε is the surface emissivity; Ts (K) is the land surface temperature and σ is the Steffan-Boltzmann constant (5.67 × 10 −8 W m −2 K −4 ). The latent heat flux (LET) depends on the evaporative fraction (Λ) and is given as follows: The evaporative fraction concept (Λ) was proposed by [16], adapted and tested by [8,18], and it is described by the equation below: where T H (K) is the temperature corresponding to dry condition and T LE (K) is the temperature corresponding to wet condition. This method can be only applied when the atmospheric conditions are constants over the image and the study site includes simultaneously wet and dry areas [8,16,18]. Besides of that, this method works better in a homogeneous vegetated area -with higher variance between dry and wet pixels.

Daily Evapotranspiration
Remote sensing data provides instantaneous radiation measurements. However, for agriculture and environment applications the evapotranspiration values are more useful. So, daily ET is defined as the temporal integration of ET instantaneous values in a day. The daily ET can be obtained using the Cdi, which consists of the ratio between the daily net radiation flux (Rnd) and instantaneous radiation flux (Rni), both from the tower flux. This concept was also adopted by Gómez et al. (2005) and Sobrino et al. [17,18]. Thus, Cdi was calculated through the integration of the radiation for the whole day: Afterwards, the daily ET (mm/day) can be written as follows: ET = (Λ Rn Cdi) 0.035265 (6) where the soil heat flux (G) was not included according to [25] assuming that much of the energy that enters the soil during the day returns to the atmosphere at night through terrestrial longwave radiation.

Data Used in the Model
In this section the inputs used in this study, including satellite and meteorological data, are presented. Table 1 shows the information about resolution, data source and variables calculated, they are all explained in the subsections.  (2) the Thermal Infrared Sensor (TIRS). The OLI images from visible to short-wave infrared and TIRS has thermal images of two-channels [26]. We acquired 22 cloud free Landsat 8 OLI and TIRS images, from 2015 and 2019, for the temporal and comparative analysis, the images passage occurs at 13:25 UTC. A Landsat 8 scene size is 185 km × 180 km, however the images were cut to a mask covering the study area, where the flux tower is located, covering mostly by a native vegetation of the Pampa biome with controlled cattle management. Table 2 shows all days of the years and the season of the images used in this study. The Landsat data cover 185 km × 180 km Level 1 terrain-corrected products, in which the spatial resolution of TIRS bands are 100 m and resampled by cubic convolution to 30 m to be co-registered with the 30 m OLI spectral bands [27]. Also, Landsat 8 OLI surface reflectance Level-2 products are generated at the Earth Resources Observation and Science (EROS). The EROS Science Processing Architecture (ESPA) on-demand interface corrects satellite images for atmospheric effects to create Level-2 data products. These Level 2 products were used in this research to obtain the normalized difference vegetation index (NDVI) and surface albedo.

Meteorological Data
Two meteorological databases were used to produce Rn and Ts of this study: (1) The Brazilian Meteorological Institute (Instituto Nacional de Meteorologia-INMET), located in Santa Maria city near 4 km from the study area, has provided: air temperature (Ta), atmospheric pressure (P) and relative humid (RH); (2) The National Centers for Environmental Prediction Climate (NCEP) Forecast System Version 2 (CFSv2) has provided reanalysis data, including the shortwave downward radiation (R S ) and longwave downward radiation (R L ). All the meteorological data were acquired to coincide with the time and date of the satellite passage.
We extracted the reanalysis data from the CFSv2 hourly product. The parameters were obtained with 0.205 • horizontal resolution for an average between 13-14 h UTC on selected dates. From INMET Atmosphere 2020, 11, 1059 6 of 18 the data were acquired at 12 UTC on the same selected dates. The solar radiation does not vary too much in two hours, so it is assumed the variation of the instantaneous measurements in this small period is not significant [7,16].

Variables Input of S-SEBI
To estimate the balance energy by remote sensing models some pre-processing of image data are needed and some surface properties had to be calculated. Table 3 shows the algorithms used to calculate Normalized Difference Vegetation Index (NDVI), Albedo (α), Soil Heat Flux (G), Land Surface Temperature (Ts), which is dependent on water vapor (w), and Land Surface Emissivity (ε). All these variables were calculated for the whole study area by remote sensing process. Table 3. Equations applied to Landsat-8 data.

Land Surface Temperature of S-SEBI Model
To analyze the influence that possible uncertainties in the estimation of Ts may have on the estimates of LET, a noise was applied to the Ts images, with a Gaussian variation of −2 K and +2 K. Many authors believe that Ts retrieval precision varies around 1-2 K depending on the heterogeneity atmospheric conditions and the resolution of the sensor used in the process [26,[34][35][36].
It is important to emphasize that, with this noise, the average Ts of the images does not vary, but the minimum and maximum temperatures do, as we can see in Table 4.  The eddy covariance, EC, Aubinet et al. method [37] was used in the high-frequency data (10 Hz) for the determination of latent heat flux (LE) and sensible heat flux, both turbulent fluxes, over 30-min block average using EddyPro ® software version 6.1 (LI-COR). with the configurations described in [7]. The footprint analyses of the EC data by Kljun et al. [38] indicates that about 90% of the flux originated within a circle with a radius of 115 m centered in the flux tower.
The daily mean of the fluxes was used to close the energy balance throughout the Bowen ratio approach [39], generating a corrected LE. More details about the experimental site and flux data processing are described in Rubert et al. [7]. We have evaluated experimental flux data in days with clear sky conditions between 2014 and 2019 and only in dates with less than 2 h missing data.

Statistical Analyses
To assess the model's accuracy and to compare the model with and without the noise applied, we used the ratio of estimated and observed values, coefficient of determination (r 2 ), mean bias error (Bias) (Equation (7)), root mean square error (RMSE) (Equation (8)), and mean standard deviation (MSD) (Equation (9). RMSE is the overall error in the predictions relative to the actual measured value, while MAE measures the average magnitude of the errors in a set of predictions (without considering their direction), and r 2 determines the strength of the linear relationship between estimates and measurements [40,41]. Furthermore, we used the Student's t-test (with a 95% confidence level) to evaluate the significance of the linear relationship between observed and estimated values [41,42]

S-SEBI Validantion
The energy balance components estimated with S-SEBI and in situ measurements are shown in Figure 2 considering all scenes available.

Statistical Analyses
To assess the model's accuracy and to compare the model with and without the noise applied, we used the ratio of estimated and observed values, coefficient of determination (r 2 ), mean bias error (Bias) (Equation (7)), root mean square error (RMSE) (Equation (8)), and mean standard deviation (MSD) (Equation (9). RMSE is the overall error in the predictions relative to the actual measured value, while MAE measures the average magnitude of the errors in a set of predictions (without considering their direction), and r 2 determines the strength of the linear relationship between estimates and measurements [40,41]. Furthermore, we used the Student's t-test (with a 95% confidence level) to evaluate the significance of the linear relationship between observed and estimated values [41,42]

S-SEBI Validantion
The energy balance components estimated with S-SEBI and in situ measurements are shown in Figure 2 considering all scenes available.  The net radiation (Rn) measurements are the most accurate measurements of all the components in the surface energy budget, and they represent the largest part of the global radiation [39]. We have found a strong coefficient of correlation (0.81), the data produced the worst estimates of RMSE and Bias, with 138.7 (W/m 2 ) and 132.12 (W/m 2 ), respectively. Those results may be influencing the results of LE, because when Rn reaches more than 350 W/m 2 the latent heat flux tend to deviate. Besides of that, some authors have discussed that in days with no clouds and Rn less than 200 W/m 2 (mostly during the winter season) the model represents better all the fluxes [7]. Schirmbeck et al. [43] obtained a RMSE of 50 (W/m 2 ), and Silva Oliveira et al. [44] testing METRIC model in Brazilian Cerrado obtained a RMSE of 59.8 (W/m 2 ) with an overestimation of 9%.
The soil heat flux (G) is responsible for lower energy consumption, representing less than 10% in studied in pampa biome [43,45,46]. The model used in our study to produced G overestimate all the flux tower measurement, and they have produced the estimation of RMSE and Bias with 43.45 (W/m 2 ) and 40.4 (W/m 2 ), respectively. Gomis-Cebolla et al. [47] have validated four ET models, including SEBS in tropical forests of the Amazonian region, and they have concluded that their results serve to emphasize the need to improve the accuracy of reanalysis estimates in order to improve the accuracy in ET estimates. Therefore, the reanalysis data may be inserting minimums errors in our model as well.
According to Twine et al. [39] and Silva Oliveira et al. [44] LE tends to be underestimated by EC method due to sources of errors such as non-homogeneous surface coverage, soil characteristics, instrumental errors, topography, divergence or flux dispersion, among others. In LE analyzes, we have obtained mean errors (RMSE) around 92 (W/m 2 ) and Bias 7.09 (W/m 2 ), which agree with previous studies in Pampa biome of Schirmbeck et al. that obtained an overestimation of 94 (W/m 2 ) testing OSEB and SEBAL models for 84 MODIS images between 2009-2011. Those uncertainties associated with derived LE could be caused especially because of the evaporative fraction component which is limited by the selection of dry and wet pixels [48]. A physically based two-source energy balance (TSEB) model was tested in an irrigated agricultural area in China applied to high resolution WiDAS data and ASTER data and compared with EC measurements, to LE the authors found Bias and RMSE as 113 W/m 2 and 140 W/m 2 , respectively [12].

Heterogeneity of the Study Area
The performance of applying remote sensing data to ET calculation is related to the concept of spatial variability of the landscape, especially in selecting the spatial resolution of the sensor. Low spatial resolution sensors, in more heterogeneous landscapes, generate less reliable ET results since intra-pixel spatial heterogeneity is lost due to radiometric signal integration [9,[49][50][51][52]. Besides the importance of the choice of the satellite sensor, Gibson et al. [9] studied the variability of ET influenced by heterogeneity of landcover, analyzing topography, fractional vegetation cover, NDVI and albedo, the authors found uncertainties which are translated to the estimation of actual evapotranspiration. In Brazil, a study performed at Caatinga has proved that the land use, substantially affects the components of the net radiation that depend on the type and state of the land surface cover, such as reflected shortwave radiation and emitted longwave radiation [53].
In order to understand the heterogeneity and seasonality of the study area in our site, Figure 3 shows an example of NDVI distribution for each season, in which it can be seen the differences between summer/spring and winter/autumn. The most homogeneity in the area occurred in winter season. This behavior can be responsible for the high seasonal variability of evapotranspiration, with higher values during the spring-summer period when compared to autumn-winter observed in Pampa biome by [7].
The ET variability by the landcover heterogeneity are shown in Figure 4 where three different land uses were selected and the averages ET of each one was calculated. We compared the differences between Native Grassland, Exposed Soil and Forest with the daily ET average for each day. The daily ET seasonality in summer is twice as high as in winter, which was already expected because of the high temperature variability at different times of the year, characteristic of the study region. The ET variability by the landcover heterogeneity are shown in Figure 4 where three different land uses were selected and the averages ET of each one was calculated. We compared the differences between Native Grassland, Exposed Soil and Forest with the daily ET average for each day. The daily ET seasonality in summer is twice as high as in winter, which was already expected because of the high temperature variability at different times of the year, characteristic of the study region.
Gibson et al. [9] reported that in addition to the direct effect of landscape heterogeneity and spatial resolution of input data on remote sensing variables, landscape heterogeneity can also indirectly affect spatial modelling efforts, including the energy fluxes. The ET variability between Forest and Grassland were lower than expected, demonstrating the importance of native grasslands in the Pampa biome regarding to the processes of the hydrological cycle, since it covers 63% of Rio Grande do Sul, with the greatest differences occurring randomly during the warmer and colder seasons. It is important to emphasize that the native grassland area of this study has an adequate livestock management controlled by the Federal University of Santa Maria. Studies conducted in field areas  The ET variability by the landcover heterogeneity are shown in Figure 4 where three different land uses were selected and the averages ET of each one was calculated. We compared the differences between Native Grassland, Exposed Soil and Forest with the daily ET average for each day. The daily ET seasonality in summer is twice as high as in winter, which was already expected because of the high temperature variability at different times of the year, characteristic of the study region.
Gibson et al. [9] reported that in addition to the direct effect of landscape heterogeneity and spatial resolution of input data on remote sensing variables, landscape heterogeneity can also indirectly affect spatial modelling efforts, including the energy fluxes. The ET variability between Forest and Grassland were lower than expected, demonstrating the importance of native grasslands in the Pampa biome regarding to the processes of the hydrological cycle, since it covers 63% of Rio Grande do Sul, with the greatest differences occurring randomly during the warmer and colder seasons. It is important to emphasize that the native grassland area of this study has an adequate livestock management controlled by the Federal University of Santa Maria. Studies conducted in field areas Gibson et al. [9] reported that in addition to the direct effect of landscape heterogeneity and spatial resolution of input data on remote sensing variables, landscape heterogeneity can also indirectly affect spatial modelling efforts, including the energy fluxes. The ET variability between Forest and Grassland were lower than expected, demonstrating the importance of native grasslands in the Pampa biome regarding to the processes of the hydrological cycle, since it covers 63% of Rio Grande do Sul, with the greatest differences occurring randomly during the warmer and colder seasons.
It is important to emphasize that the native grassland area of this study has an adequate livestock management controlled by the Federal University of Santa Maria. Studies conducted in field areas with high exploitation management have obtained greater differences in water balance results when compared with forested areas [54].
The seasonality of the Pampa biome, Figure 5, was explained by preview studies which discussed the strong seasonality of ET in the region, with the highest rates of ET in the summer and spring period [7,43,55,56]. In warmer periods there is usually higher energy availability, rapid vegetation development, higher biomass accumulation, which also indicates a higher ET [43]. During the colder seasons (autumn and winter), the small growth in the Pampa grasslands all of the biomass production is consumed by cattle, which is typical in this biome [57]. In this sense, an adequate land use management is essential for the maintenance of native species in the region that also favor livestock farming and are dependent on water cycle.
with high exploitation management have obtained greater differences in water balance results when compared with forested areas [54].
The seasonality of the Pampa biome, Figure 5, was explained by preview studies which discussed the strong seasonality of ET in the region, with the highest rates of ET in the summer and spring period [7,43,55,56]. In warmer periods there is usually higher energy availability, rapid vegetation development, higher biomass accumulation, which also indicates a higher ET [43]. During the colder seasons (autumn and winter), the small growth in the Pampa grasslands all of the biomass production is consumed by cattle, which is typical in this biome [57]. In this sense, an adequate land use management is essential for the maintenance of native species in the region that also favor livestock farming and are dependent on water cycle.

The Ts Influence on S-SEBI Model
The errors or uncertainties in analysis of remote sensing and GIS products can be associated with several sources. According to Gibson et al. most of them are: (1) associated with the specific remote sensing data obtained; (2) introduced with the processing and analysis of image and field data; (3) associated with positional aspects (including image resolution); and (4) associated with the specific model. In this regard, the uncertainties in the derivation of ET for this study were identified in the relationship between Ts and albedo for the S-SEBI model performance for the selected days between 2015-2019. In addition, there is an influence of Rn on LE results, discussed in Section 3.1, and consequently on ET. Table 5 shows the comparison of energy partitioning between S-SEBI results with and without noise in the Ts in a native grassland. The minimum and maximum values in the fluxes have changed when the noise was applied, LE flux has the highest shift, the difference decreases 11%, while in the other flows the changes did not cause significant differences, less than 1%. This is because LE is based on the correct selection of hot and cold pixels which are highly dependent on Ts values, this dependence is strongly studied by several authors [6,8,58,59].

The Ts Influence on S-SEBI Model
The errors or uncertainties in analysis of remote sensing and GIS products can be associated with several sources. According to Gibson et al. most of them are: (1) associated with the specific remote sensing data obtained; (2) introduced with the processing and analysis of image and field data; (3) associated with positional aspects (including image resolution); and (4) associated with the specific model. In this regard, the uncertainties in the derivation of ET for this study were identified in the relationship between Ts and albedo for the S-SEBI model performance for the selected days between 2015-2019. In addition, there is an influence of Rn on LE results, discussed in Section 3.1, and consequently on ET. Table 5 shows the comparison of energy partitioning between S-SEBI results with and without noise in the Ts in a native grassland. The minimum and maximum values in the fluxes have changed when the noise was applied, LE flux has the highest shift, the difference decreases 11%, while in the other flows the changes did not cause significant differences, less than 1%. This is because LE is based on the correct selection of hot and cold pixels which are highly dependent on Ts values, this dependence is strongly studied by several authors [6,8,58,59].
This difference in LE estimations are demonstrated by statistical analyses with a RMSE 19.36 W/m 2 and Bias 11.48 (W/m 2 ), this result is lower than other models reported in the literature, which are more dependent on meteorological data. Su (2002) [60] found out a sensitivity of SEBS model around 40 W/m 2 when the various terms are assumed independent of each other.
The differences in the other fluxes when the noise in Ts is applied are not significant, with extremely low errors and variances as RMSE (1.98 and 0.27) and Bias (1.97 and 0.24) to Rn and G, respectively. Table 5. Comparison between energy fluxes with and without noise in a native grassland (in situ data): Min-Max is minimum and maximum values, r 2 is the coefficient of determination (-), MSD is the mean standard deviation (W/m 2 ), RMSE refers to the Root Mean Square Error (W/m 2 ); and Bias is the tendency of the model (W/m 2 ).

Variable
Min

The Ts Influence on Daily Evapotranspiration
The natural grassland daily ET mean error between both analyses (with and without noise in Ts) is 0.18 mm/day for the whole period studied, those variance to each day at tower flux point are shown in Figure 6. Gibson et al. [9] have analyzed the SEBS model, and conclude that daily ET differences by up to 0.7 mm/day when modifying Ts and air temperature. We concluded that the gaussian variation of Ts (between −2 K and 2 K) leads to a small variation of ET, it does not exceed 0.5 mm/day in grasslands. Abid et al. [10] are in accordance with this result finding similar value (0.5 mm/day) when comparing de uncertainties of SEBS model in Northern Tunisia. data): Min-Max is minimum and maximum values, r 2 is the coefficient of determination (-), MSD is the mean standard deviation (W/m 2 ), RMSE refers to the Root Mean Square Error (W/m 2 ); and Bias is the tendency of the model (W/m 2 ).

Variable
Min-Max This difference in LE estimations are demonstrated by statistical analyses with a RMSE 19.36 W/m 2 and Bias 11.48 (W/m 2 ), this result is lower than other models reported in the literature, which are more dependent on meteorological data. Su (2002) [60] found out a sensitivity of SEBS model around 40 W/m 2 when the various terms are assumed independent of each other.
The differences in the other fluxes when the noise in Ts is applied are not significant, with extremely low errors and variances as RMSE (1.98 and 0.27) and Bias (1.97 and 0.24) to Rn and G, respectively.

The Ts Influence on Daily Evapotranspiration
The natural grassland daily ET mean error between both analyses (with and without noise in Ts) is 0.18 mm/day for the whole period studied, those variance to each day at tower flux point are shown in Figure 6. Gibson et al. [9] have analyzed the SEBS model, and conclude that daily ET differences by up to 0.7 mm/day when modifying Ts and air temperature. We concluded that the gaussian variation of Ts (between −2 K and 2 K) leads to a small variation of ET, it does not exceed 0.5 mm/day in grasslands. Abid et al. [10] are in accordance with this result finding similar value (0.5 mm/day) when comparing de uncertainties of SEBS model in Northern Tunisia.  Figure 7 shows the resulting changes in Mean, Maximum and Minimum ET against Ts considering all scene. The gaussian noise applied is a random noise, so it is probable that the maximum Ts pixel value of an image is not the same as in the noisy image, therefore the maximum and minimum are modified in more than a 2 K noise applied. The differences in maximum and minimum Ts caused by the noise applied affect ET values, but the mean ET are less affected by these differences on mean Ts of the scenes. The biggest differences on mean ET occurred on summer in 2015 with 0.44 mm/day, but the minimum and maximus ET have generated the biggest changes, these values occurred in forest or in exposed soil areas. The changes in maximum and minimum ET were expected because S-SEBI model has difficulty in reaching extremely high values [18,47].  Figure 7 shows the resulting changes in Mean, Maximum and Minimum ET against Ts considering all scene. The gaussian noise applied is a random noise, so it is probable that the maximum Ts pixel value of an image is not the same as in the noisy image, therefore the maximum and minimum are modified in more than a 2 K noise applied. The differences in maximum and minimum Ts caused by the noise applied affect ET values, but the mean ET are less affected by these differences on mean Ts of the scenes. The biggest differences on mean ET occurred on summer in 2015 with 0.44 mm/day, but the minimum and maximus ET have generated the biggest changes, these values occurred in forest or in exposed soil areas. The changes in maximum and minimum ET were expected because S-SEBI model has difficulty in reaching extremely high values [18,47]. When there are uncertainties in estimates of Ts, the errors in the estimates of the daily ET multiply for the entire study area, as shown in Figure 8, the maximum and minimum values of Ts are responsible for the variation in the ET estimated, even with the same mean Ts for the images. We can see that Ts have biggest range during summer seasons and on winter seasons de maximum and minimum Ts are closer, but that differences do not influence the changes in daily ET. These results demonstrate the importance of Ts' accuracy in the selection of the driest and wettest pixels, thus being the greatest challenge in applying S-SEBI to estimate ET season-independent even though the seasonal variability of ET.  When there are uncertainties in estimates of Ts, the errors in the estimates of the daily ET multiply for the entire study area, as shown in Figure 8, the maximum and minimum values of Ts are responsible for the variation in the ET estimated, even with the same mean Ts for the images. We can see that Ts have biggest range during summer seasons and on winter seasons de maximum and minimum Ts are closer, but that differences do not influence the changes in daily ET. These results demonstrate the importance of Ts' accuracy in the selection of the driest and wettest pixels, thus being the greatest challenge in applying S-SEBI to estimate ET season-independent even though the seasonal variability of ET. When there are uncertainties in estimates of Ts, the errors in the estimates of the daily ET multiply for the entire study area, as shown in Figure 8, the maximum and minimum values of Ts are responsible for the variation in the ET estimated, even with the same mean Ts for the images. We can see that Ts have biggest range during summer seasons and on winter seasons de maximum and minimum Ts are closer, but that differences do not influence the changes in daily ET. These results demonstrate the importance of Ts' accuracy in the selection of the driest and wettest pixels, thus being the greatest challenge in applying S-SEBI to estimate ET season-independent even though the seasonal variability of ET.

Discussion
Many studies have been carried out in the Pampa biome with the objective of understanding how different agricultural management affects this ecosystem [15,22,57,[61][62][63][64], but few studies are aimed how the energy balance is affected by these activities [7,43,56,65,66]. It is important to emphasize that the native grassland of Pampa biome is important not only for the preservation of the biodiversity of endemic species in the region, but also for the sustainable development of rural families [19,22,67,68]. In this sense this work brings a new variable to this equation, that the native grasslands with adequate management are so important for the energy balance as the forests found in the region.
According to Fontana et al. [49] the weather station affects and modifies the accumulation of forage in the natural grasslands of the Pampa biome, which is typical of the subtropical climate prevailing in the region. In this sense, winter is the critical season for livestock production, which corroborates with the results of this work that demonstrates the decrease of evapotranspiration in winter indicating less forage production.
Some complexities associated with the derivation of ET and discussed by Gibson et al. [9] imply that potential errors will be introduced at various stages of ET derivation, including the heterogeneity of the area and meteorological data. From the energy point of view, evapotranspiration is dependent on latent heat flux. It is in this context that the models (such as SEBAL, S-SEBI, SEBS, SEBTA, SAFER) that calculate ET by remote sensing are based. In this study we used S-SEBI which depends mainly on the relationship between albedo and Ts. This is the first study developed in the Pampa biome that seeks to understand the influence of the Ts on energy balance fluxes and daily ET, some studies have been developed with the objective of understanding the environmental and atmospheric influences on remote sensing evapotranspiration models, but none of them evaluate the S-SEBI [9,10,60].
The accuracies of most Ts retrieval algorithms are between 1 and 2 K [26,36,69]. In this sense, this work demonstrates that for the S-SEBI model, although these differences in temperature affect the choice of hot and cold pixels of images and to estimate LE, the possible errors generated by retrieve Ts and emissivity do not affect the results in daily evapotranspiration so significantly (0.5 mm/day). Also, the method used in the conversion of LE to daily ET, explained in the Section 2.3, contributes to reduce the errors of the one-time estimate, because it considers the global radiation behavior throughout the day [18].

Conclusions
In order to estimate daily evapotranspiration (ET) using S-SEBI model and remote sensing technologies from Landsat 8, a sensitivity study of output ET was performed with a Gaussian noise variability in LST images. The S-SEBI model estimates ET from the relationship between LST and albedo. This study allowed to understand the influence that the uncertainties in LST estimation may have on the ET.
The accuracy of the Rn validation has aggregated some uncertainties in the model, (more than 100 W/m 2 ), these errors might be related to the use of reanalysis data. Therefore, an evaluation regarding the sensibility of this data on energy balance models is indicated for future works.
The lower ET variability between forest and native grassland can demonstrate the importance of native grasslands in the Pampa biome regarding to the processes of the hydrological cycle, since it covers 63% of Rio Grande do Sul. It also indicates that in Pampa biome the native grassland is not only important to the biodiversity conservation but also to the environment process. Future studies may provide more conclusions about the influences of different native grasslands managements.
The gaussian variation of LST (between −2 K and 2 K) do not influence the average of the variable and leads to a small variation of ET, it does not exceed 0.5 mm/day in grasslands, with mean error between both analyses (with and without noise in LST) around 0.18 mm/day for the whole period studied.
We concluded that the S-SEBI is less dependent on LST estimation than other models reported in the literature, such as the SEBS largely studied [9,10]. However, the importance of LST's accuracy in the selection of driest and wettest pixels was proved. Funding: This research was funded in part by the Coordenação de Aperfeiçoamento de Pessoal de Nível Superior-Brazil (CAPES), finance code 001, Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq) and Fundação de Amparo à Pesquisa do Rio Grande do Sul (FAPERGS). We are also grateful to the anonymous reviewers for the valuable comments.