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The Use of MODIS Images to Quantify the Energy Balance in Different Agroecosystems in Brazil The Use of MODIS Images to Quantify the Energy Balance in Different Agroecosystems in Brazil

Sugarcane (SC) is expanding over coffee (CO), while both crops have replaced the natural vegetation (NV) in the northeastern side of São Paulo (SP) state, Southeast Brazil. Under these dynamic land-use changes, geosciences are valuable tools for evaluating the large- scale energy and mass exchanges between the vegetation and the lower atmosphere. For quantification of the energy balance components in these mixed agroecosystems, MODIS images were used throughout the Simple Algorithm for Evapotranspiration Retrieving (SAFER) algorithm, during the year 2015 in the main sugarcane- and coffee-growing regions of the state. Regarding, respectively, sugarcane, coffee, and natural vegetation, the fractions of the net radiation (Rn) used as latent heat flux (λE) were 0.68, 0.87, and 0.77, while the corresponding ones for the sensible heat (H) fluxes were 0.27, 0.07, and 0.16. Negative H values were noticed from April to July, because of heat advection rais- ing λE values above Rn, but they were more often in coffee than in sugarcane. It was concluded that sugarcane crop presented lower evapotranspiration rates, when com- pared with coffee, which could be an advantage under the actual water scarcity scenario. However, sugarcane replacing natural vegetation means environmental warming, while the land use changes promoted by coffee crop represented cooling conditions.


Introduction
Sugarcane (SC) (Saccharum officinarum) and coffee (CO) (Coffea arabica L.) crops are expanding in the northeastern side of the São Paulo (SP) state, Southeast Brazil. The first one is an annual crop, while the second one is a perennial crop, but both are replacing the natural vegetation (NV), composed by a mixture of Savannah and Atlantic Coastal Forest species. However, sugarcane is also replacing the coffee areas [1], as consequences of both sugar and alcohol explorations, but also by stimulating renewable energy use [2].
The negative effects of the sugarcane expansion could be more serious when compared with those from the fossil fuel exploration, regarding greenhouse gas emissions [3,4]. Aiming bioenergy production, a crop has to grow fast presenting high yield, but its energy output must exceed fossil fuel energy input. Considering these issues, sugarcane is a good candidate for energy crop [5]. However, its expansion could affect the large-scale energy balance further influencing the carbon cycle [6][7][8]. Anderson-Teixeira et al. [9] have reported energy balance alterations because of sugarcane expansion.
Under land-use and climate change conditions, the use of tools for quantifying the large-scale energy balance components is relevant for supporting policy planning and decision-makings about the water resources. The difficulties of measuring and analyzing these components throughout only field measurements highlighted the importance of coupling remote sensing and weather data, which have been successfully done in commercial crops under different environmental conditions [3,10].
Several algorithms have been developed for acquiring the large-scale energy balance components. The Simple Algorithm for Evapotranspiration Retrieving (SAFER) is applied in this chapter in sugarcane and coffee crops comparing the results with those for natural vegetation. The algorithm was developed and validated in Brazil based on simultaneous field radiation and energy balance data from experiments and remote sensing under strongly water and vegetation contrasting conditions [11,12].
Having cropland masks available, the energy balance components are analyzed in these mixed agroecosystems by the coupling MODIS images and weather data. The results may subsidize policies for a rational sugarcane and coffee water managements, being the analyses very useful under the actual scenario of water competitions between these crops and other sectors in the Southeast Brazil, as consequences of both climate and land use changes. Figure 1 shows the location of the study region in the northeastern side of São Paulo state, Southeast Brazil, together with the cropland masks and the agrometeorological stations used for the weather data gridding processes.

Study region, crops, and agrometeorological data
The agroecosystems are constituted by sugarcane (SC) and coffee (CO) interspaced with natural vegetation (NV). This last class is a mixture of Savannah and Atlantic Coastal Forest species. Some of the areas before occupied by coffee are nowadays being replaced by sugarcane crop.
The sugarcane areas present two well-defined seasons: the first one rainier and hotter and the other one drier and colder. According to Cabral et al. [13], the long-term maximum rainfall occurs in December (274 ± 97 mm month −1 ), and the minimum one is between July and August (27 ± 34 mm month −1 ); the annual value is 1517 ± 274 mm yr. −1 . The mean air temperatures in January and July are, respectively, 24 and 19°C, and the annual average is 22°C.
The sugarcane phases may be divided into four [14]: Phase 1: Germination and establishment, from January to February, are influenced by soil moisture, soil temperature, and soil aeration, denoting activation and subsequent sprouting of the vegetative bud. Phase 2: Tillering is influenced by variety, solar radiation, air temperature, soil moisture, and fertilization, starting from around 40 days after the initiation of the growing cycle and may last up to 120 days (February-April). Phase 3: Grand growth is from 120 days after the starting of the growing cycle lasting up to 270 days in a 12-month crop (May-September). Both high soil moisture and solar radiation levels favor better cane elongation during this phase. Phase 4: Ripening and maturation are characterized by slower growth activity, lasting for about 3 months starting from 270 to 360 days after the growing cycle initiation (September-December). High solar radiation levels and low soil moisture conditions are favorable during this last phase [15].
The coffee crop concentrates at the right side of the study area (see Figure 1). The region presents also a rainy season and a dry winter somewhat similar to the sugarcane areas; however, due to higher altitudes, between 700 and 1100 m, the long-term annual air temperature ranges are lower, from 18 to 20°C [16].
The coffee crop in Brazil, differently from sugarcane, which completes its average growing cycle in 12 months, takes 2 years for its all crop stages. Six coffee phases are considered, starting in September of each year [17,18]: Phase 1: Vegetation with bud formation, during 7 months, is normally from September to March. Phase 2: Vegetation is between April and August, when the transformation of the vegetative to reproductive buds occurs, when at the end of this phase, from July to August, the plants enter in relative dormancy stage. Phase 3: Flowering and grain expansion are normally from September to December. Phase 4: Grain formation is normally from January to March, when water stress can be detrimental to the grain development. Phase 5: Grain maturation. Moderate water stress can benefit the grains. Phase 6: Senescence and death of the non-primary productive branches generally occur in July and August. In this last stage, the self-pruning process represented by senescence occurs, when the productive branches wither and die, limiting plant development.   Figure 2. Flowchart for modeling the energy balance throughout application of the SAFER algorithm to the MODIS MOD13Q1 product.

Large-scale energy balance modeling
For the large-scale modeling, the MODIS images were used during the year 2015 together with 10 agrometeorological stations from the National Meteorological Institute (INMET) in the study area, considering the cropland classes. Weather data were used to calculate the reference evapotranspiration (ET0) by the Penman-Monteith method [19]. The weather input modeling parameters, global solar radiation (RG), air temperature (T a ), and ET 0 were up scaled for the 16-day period of the MODIS MOD13Q1 reflectance product (spatial resolution of 250 m) and gridded by using the moving average method generating pixels with the same spatial resolution as the satellite images. Figure 2 shows the steps for modeling the energy balance throughout the SAFER algorithm with the MODIS MOD13Q1 product.
Following Figure 2, the surface albedo (α 0 ) was estimating according to Valiente et al. [20]: where α 1 and α 2 are the reflectances from the bands 1 and 2, respectively, and a, b, and c are regression coefficients, considered as 0.08, 0.41, and 0.14, obtained under different Brazilian vegetation types and distinct hydrological conditions [10].
The normalized difference vegetation index (NDVI) is a measure of the amount of vegetation at the surface: The reflected solar radiation (R R ) was estimated as The longwave atmospheric radiation (R a ) was calculated by applying the Stefan-Boltzmann low: where ε A is the atmospheric emissivity and σ is the Stefan-Boltzmann constant (5.67 × 10 −8 W m −2 K −4 ).
The parameter ε A was calculated according to Teixeira et al. [21]: where τ is the shortwave atmospheric transmissivity calculated as the ratio of R G to the incident solar radiation at the top of the atmosphere and a A and b A are the regression coefficients 0.94 and 0.10, respectively.
Net radiation (Rn) can be described by the 24-hour values of net shortwave radiation, with a correction term for net longwave radiation [22]: where a L is the regression coefficient of the relationship between net longwave radiation and τ on a daily scale.
Because of the thermal influence on longwave radiation via the Stephan-Boltzmann equation, a L coefficient from Eq. (6) was correlated with the 24-hour T a [11]: where d and e are the regression coefficients found to be 6.99 and 39.93, respectively.
Having estimated R R , R a , and Rn, the emitted surface longwave radiation (R s ) was acquired as residue in the radiation balance equation: Then, the surface temperature (T 0 ) was estimated by the residual method [22]: where the surface emissivity (ε S ) was estimated as follows [22]: and a S and b S are the regression coefficients 0.06 and 1.00, respectively.
The SAFER algorithm is used to model water indicator represented by the ratio of the actual to the reference evapotranspiration (ET r ) based on the input remote sensing parameters, which is then multiplied by the 24-hour ET 0 values to estimate the daily ET large-scale rates which in turn are transformed into latent heat fluxes (λE): where f and g are the original regression coefficients, 1.8 and −0.008, respectively. The correction factor (ET0 yr /5) is applied, ET0 yr being the annual grids of reference evapotranspiration for São Paulo state in the year 2015 and 5 mm is the ET 0yr value for the period of the original modeling in the Northeast Brazil [21].
For soil heat flux (G), the equation derived by Teixeira [12] was used: where the regression coefficients a G and b G are 3.98 and −25.47.
The sensible heat flux (H) is acquired as residue in the energy balance equation:

Thermohydrological conditions and crop stages
The driving weather variables for the surface energy balance are R G , T a , precipitation (P), and ET 0 . They are presented in Figure 3  Among the four weather parameters, P was the most variable along the year with the largest values occurring during the first and the last 3 months. The high-moisture conditions in the root zones during these periods affect the energy balance, increasing the latent heat fluxes (λE) for all agroecosystems. The rainfall annual totals were 1253, 1277, and 1245 mm yr −1 for the sugarcane (SC), coffee (CO), and natural vegetation (NV) with the range of standard deviation (SD) staying between 11 and 12 mm yr −1 . These values are below the historical value of the study area, and they were not well distributed along the year. A period from July to October, with several rainfall 16-day values bellow 10 mm, was noticed for all analyzed agroecosystems. The short rainfall amounts occurred from Phase 3 to Phase 4 of the generalized sugarcane growing cycle, which should have caused some water deficit, when its water requirements are high. Cabral et al. [13] reported a 13% of sugarcane biomass reduction in relation to the regional average in São Paulo state, Brazil, because of the lower water availability observed during the initial 120 days of cane regrowth. For rainfed sugarcane crop, a well-distributed growing season total precipitation between 1100 and 1500 mm is considered adequate. However, the P dropping during Phase 3 should have caused some water deficit, when the crop water requirements are high, further affecting the energy partition, by reducing leaf area and the number of tillers and leaves per stalk [23]. During Phase 4, rains are not desirable for sugarcane, because they lead to poor juice quality [15], and then the high amounts at the end of the year, coinciding with this phase, were not favorable.  from May to July, coincide with the sugarcane Phase 3, favoring cane elongation reduction during this phase.
In relation to R G and T a , the differences among the agroecosystems were smaller than those for P and ET 0 , with average annual values around 17 MJ m −2 day −1 and 23.0°C, respectively. Then, the highest atmosphere demands in sugarcane could be probably attributed to low air humidity and/or high wind speed conditions.
The thermohydrological conditions also strongly affect the coffee crop stages [17]. As the growing cycle takes 2 years, some coffee phases will coexist. Rainfall should be well distributed for good yield. At the start of the year, for the period involving Phases 1 and 4, there was only a 16-day (DOY 001-016) period with P lower than 10 mm in January. In Phase 2 rainfall is important for the transformation of the vegetative to reproductive buds. During this period, P declined until values close to zero at the end of July (DOY 209-224). In Phase 3 (September-November), some water stress is desirable, as the main flowering happens during a period of water stress following by good water availability. However, only two 16-day periods with low rainfall amounts are verified from September to October (DOY 257-288).
In Phase 4, water stress may wilt the fruits, but only during the period from DOY 001 to 016 the rainfall amount was low, bellow 10 mm. In Phase 5 the water requirements declined, and some water deficit during this phase could have favored the coffee plant growth. The period with low rainfall amounts from May to June was also inside this phase.
Conditions of low R G and ET 0 levels from May to August coincided with low P amounts, thus reducing water consumption in coffee areas. Air temperature (T a ) regulates the vegetative growth and reproductive buds, being high values associated with water deficit during booming the reason for flower abortion and growth reduction [23]. However, the higher values, above 23°C, occurred under conditions of good rainfall availability. Regarding the ratio Rn/RG (Figure 5b), the higher mean pixel values were for the coffee (CO) class, mainly in the middle of the year. The values ranged from 0.49 to 0.55, from 0.50 to 0.57, and from 0.50 to 0.56, for, respectively, the SC, CO, and NV agroecosystems. The average annual Rn/RG of 50-55% is in agreement with field measurements in fruit crops and natural vegetation in the Northeast Region of Brazil [11] and with studies involving other distinct agroecosystems around the world [24,25]. These results of similarities with national and international studies give confidence to the large-scale remote sensing methods tested here by coupling the MOD13Q1 product and agrometeorological stations.     Figure 6.

Agroecosystem energy balances
Much more distinct of both λE and SD values among the agroecosystems are noticed than in the case of Rn, with λE ranging from close to zero to becoming higher than 13 MJ m −2 d −1 .
The lowest values were for the sugarcane (SC) class, with an average λE of 6.1 ± 2.2 MJ m −2 d −1 , followed by natural vegetation (NV), 6.9 ± 1.8 MJ m −2 d −1 , and coffee (CO) with the highest average of 7.8 ± 1.8 MJ m −2 d −1 . Besides the lowest λE, the SC class presented also the largest spatial variation. Considering all agroecosystems, the highest and the lowest λE rates were, respectively, in January and at the end of October.   Considering the three studied agroecosystems, the λE values started with short values, below 5.0 MJ m −2 d −1 , at the first half of January (2.0 mm d −1 ), due to the low rainfall amounts (see Figures 3a and 7a). After the first rains, λE followed the RG levels but dropping again in August because a short water scarcity spell. Clearly, one could see that in almost all periods of the year, for the coffee (CO) class, λE values were the highest ones, while for sugarcane (SC), they were the lowest ones. Natural vegetation (NV) presented intermediary λE values.
Energy balance differences among the agroecosystems were also noticed for the λE/Rn ratio. This last ratio is an index of the soil moisture in the root zones, and its behavior along the year evidenced two low-water availability periods in the root zones, with λE/R n values below 0.60. One of these conditions was at the first half of January; however, for the sugarcane (SC) class, there was a longer period with low λE/Rn, from the first half of August to the end of October, dropping below 0.20.
Considering λE in terms of mm of waters, the evapotranspiration (ET) rates were from 0.7 to 3.6 mm d −1 , from 1.2 to 4.1 mm d −1 , and from 1.2 to 3.7 mm d −1 for the sugarcane (SC), coffee (CO), and natural vegetation (NV) agroecosystems, respectively. The corresponding annual average values were 2.5, 3.2, and 2.8 mm d −1 . Eksteen et al. [26] reported ET daily values for sugarcane (SC) between 1.6 and 2.9 mm d −1 , involving different varieties and soil moisture conditions, while in Florida (USA), Omary and Izuno [27] found a daily range from 0.7 to 4.6 mm d −1 . Regarding coffee (CO) crop, Vila Nova et al. [28] reported in Brazil, for the complete grain maturation, the mean ET rates of 3.5 mm d −1 , while Oliveira et al. [29] found an average of 2.9 mm d −1 . The ET values for the SC and CO agroecosystems in the current research are similar to these national and international studies.
The higher λE values for coffee (CO) than for sugarcane (SC) in the northeastern São Paulo state, Brazil, mean a larger annual water consumption for the first crop that should be considered under the conditions of water competition by agriculture and other sectors. Even with the cropland masks involving different stages of the agroecosystems in the current study, the similarity of our Rn and λE values with those from national and international literature provides confidence for the large-scale energy balance analyses by applying the SAFER algorithm throughout the MOD13Q1 product. Taking into account all agroecosystem classes, the largest H values were during the driest conditions of the year, in the first half of January and from the second half of September to the end of October. The lowest ones, even negative, were at the end of the first rains, from April to the second half of July, when the root zones of the agroecosystems were moistier. In the middle of the year, negative H indicated horizontal heat advection from the drier and hotter natural areas to the wetter and colder cropped areas (Figure 9a)   The shapes of the curves pictured in Figure 11 were somewhat similar of those for the latent heat flux (λE), but the values for the natural vegetation (NV) class moved from intermediary to the highest values. Lower G and of its ratio to net radiation (Rn) for the sugarcane (SC) class  were found, mainly in the period of DOY 097-304 (April to the end of October). The average values of Rn partitioned as G were, respectively, 5, 6, and 7% for sugarcane (SC), coffee (CO), and natural vegetation (NV) agroecosystems.

Conclusions
The joint use of agrometeorological stations and the MODIS MOD13Q1 reflectance product allowed the large-scale energy balance quantification and analyses in the mixed agroecosystems composed by sugarcane, coffee, and natural vegetation along the year 2015 in the northeastern side of São Paulo state, Southeast Brazil. The strong dependence of net radiation (Rn) on the global solar radiation (RG) levels was clear for all classes, however, being lower for sugarcane and higher for coffee.
The daily values for the latent (λE), sensible (H), and ground (G) heat fluxes can be estimated in different kinds of vegetation from instantaneous measurements of the reflectances from the MODIS sensor, throughout the application of the SAFER algorithm. The lowest and the highest λE were, respectively, for sugarcane and coffee. Although sugarcane presents lower evapotranspiration rates than coffee crop in an annual scale, being a positive aspect under the actual water scarcity conditions, its higher H has to be considered under the conditions of the coupled effects of warming and land use changes.