The flux sites were set up in 2000 installed at a savanna ecosystem (PDG site) and a sugarcane cropland (USE site). Turbulent fluxes (H and LE) were measured at heights of 7 m (USE) and 21 m (PDG). For the 7 m height at USE, the maximum contributing area has a footprint of between 40 and 60 m, whilst for the 21 m height at PDG, it was between 120 and 170 m [58–60]. The accumulated flux for neutral conditions shows that more than 80% of measured flux at PDG site originates within 500 m, while at USE site originates within 1,500 m [58]. Turbulent flux measurements of H and LE at the USE site had calibration problems between August and December 2001 while some of the equipment o the tower installed at the PDG site had missing calibrations during January and September 2001 [58]. Ancillary meteorological data measurements needed for the analysis included R_n and G. Detailed descriptions of the equipment used, measurement procedures and results at both PDG and USE sites can be found in Juárez [60], Cabral et al. [61] and Rocha et al. [62].

The study area lies between the Brazilian States of São Paulo and Minas Gerais. The Rio Grande basin is located between latitudes 19°15´S and 23°00′S and longitudes 43°30′W and 51°00´W. Most of the basin is covered by a savanna vegetation, locally called Cerrado. This natural vegetation was extensively replaced during the last centuries by intensive production of sugarcane, soya and by pastures. Savanna ET has a strong seasonality, varying between 6 mm·day⁻¹ in the wet season to 1 mm·day⁻¹in the dry season. In agricultural areas, ET varies according to the type of the cropland and its cultivation cycle, with significant variations due to vegetation structure that may range from bare soil to fully developed canopy cover.

The MGB-IPH was applied to the Rio Grande basin (145,000 km²) while SEBAL was applied over an area of 2° × 2° (45,000 km²) selected to cover the flux tower sites. The overlay between MGB-IPH and SEBAL is about 38,100 km² (Figure 1).

Measured data (provided at half-hour) were averaged to 1-hour and to daily periods to compare with model-predicted data. We did not gap-fill with a model and we excluded any given daily average if fewer than 75% of data time steps were available. The performance of the models were evaluated based on values of root mean square error (RMSE), mean absolute error (MAE) and coefficient of determination (r² ) for model-predicted versus measured data. The 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. The r² assesses how well the model reflects the variations in the data.

SEBAL estimations were spatially averaged over a 3 × 3 1-km pixels window centred on each flux tower to achieve spatial representativeness of the measured data for each site. Instantaneous values of R_n derived from SEBAL near mid-day (Terra MODIS has a ∼11:30 am local over-passing time) significantly explained over 80% of the variation of measured values at the USE (r² = 0.88, p < 0.05) and at the PDG sites (r² = 0.83, p < 0.05) (Figure 2(a)). There was a very marked seasonality, associated with the variation in solar radiation at the earth’s surface. RMSE was 37 W·m⁻² at USE and 47 W·m⁻² at PDG. Largest errors in the estimation of R_n occurred during the wet season, when days may have been partially cloudy or when clouds were present but not detected in MOD11A1. Instantaneous values of G at USE varied between 12 and 58 W·m⁻² in dry and wet seasons, respectively, and at PDG between 8 and 24 W·m⁻². Estimated values were moderately correlated with observed data (Figure 2(b)), varying between 40 and 120 W·m⁻² at USE, and between 29 and 70 W·m⁻² at PDG, in dry and wet seasons respectively. In absolute values, G was overestimated on average by 35 and 41 W·m⁻². Estimates of H showed greater uncertainties relative to observed data. The mean instantaneous flux of H estimated by SEBAL at USE site was 217 ± 68 W·m⁻², whilst the mean value given by the EC system was 175 ± 55 W·m⁻². At the PDG site, the estimated mean was 170 ± 71 W·m⁻², compared with the observed EC mean of 179 ± 51 W·m⁻². The RMSE was 36 and 38 W m⁻² at USE and PDG sites, respectively. We found a r² of 0.60 (p < 0.05) and 0.52 (p < 0.05) at USE and PDG sites when comparing modelled H values with the in situ EC measurements (Figure 2(c)). Discrepancies in estimates of H can be explained by the combination of a series of factors related to simplifications and uncertainties introduced in algorithms to predict ET [17,63]. However these discrepancies are similar to results found by other studies [17,63–68] when validating different models for turbulent flux estimation under different conditions of land use and land cover. Although LE fluxes estimated using SEBAL showed the correct seasonal pattern, an overestimation was found. At the USE site the mean overestimation was 23 W·m⁻² with r² = 0.64 (p < 0.05), whilst at PDG overestimation was approximately 70 W·m⁻² with r² = 0.62 (p < 0.05), when comparing modelled LE values with the in situ EC measurements (Figure 2(d)). The mean estimated LE at USE was 271 ± 100 W·m⁻², whilst for the EC system the mean was 287 ± 87 W·m⁻², with RMSE 34 W·m⁻². At PDG, mean LE was estimated as 386 ± 93 W·m⁻² compared with a mean of 285 ± 122 W·m⁻² from the in situ EC data, with RMSE of 81 W·m⁻².

The energy balance closure, given by comparing the turbulent fluxes (H+LE) estimated by SEBAL with the observed available energy (R_n–G), shows an underestimation of about 7% in turbulent flux at the USE site and 9% at PDG, with r² = 0.88 (p < 0.05) and r² = 0.85 (p < 0.05) respectively (Figure 3(a)). Since the measurements and estimates of R_n, G, H and LE are found by different methods, the energy balance closure shows whether or not there is agreement between these values. The mean value of H+LE estimated by SEBAL for the USE site was 488 ± 78 W·m⁻² whilst the mean of measured R_n–G was 516 ± 68 W·m⁻². At PDG, the mean H+LE given by SEBAL was 536 ± 89 W·m⁻² compared with a mean of measured R_n–G, 589 ± 109 W·m⁻². From an analysis of energy balance closure, Juarez [60] found underestimations of 24% and 23% in observed turbulent fluxes at the sites USE and PDG respectively, suggesting that there may be limitations inherent in the EC measurement system. It is not always possible to reach a satisfactory result because of measurement errors, particularly in the EC technique, which normally underestimates turbulent fluxes because of the difference between the levels at which R_n sensors are mounted (some meters above the surface) compared with sensors for G (some centimeters below the surface), and because of surface heterogeneity [69–71].

To understand what drives estimations of ET using SEBAL algorithm, coefficients of determination (r² ) were calculated between instantaneous LE (on MODIS overpass) and the main inputs to the model (albedo, land surface temperature (T_s) and NDVI) and intermediate variables (surface emissivity (ε_s), roughness length (Z_om), gradient of temperature (dT), wind friction velocity (u_*), aerodynamic resistance (r_a) and net radiation (R_n)). Figure 4 shows: (1) the importance of NDVI for estimating LE (disregarding ε_s and Z_om since these are estimated as functions of NDVI, which explains the high correlation between these variables and LE), (2) the importance of precision in the choice of “anchor” pixels to determine dT and (3) the influence of R_n in controlling LE.

The NDVI uses spectral information at near infrared (NIR) wavelengths (between 0.7 and 1.0 μm) to measure terrestrial photosynthetic activity and structural variations in the canopy [72]. Variations in LE are quantitatively associated with spatial and temporal changes in the vegetation canopy, since under normal conditions of water and nutrient availability there is a strong negative correlation between T_s and NDVI. Although NDVI and LE are highly correlated, two factors are limiting: (i) the saturation of MODIS NDVI in areas where vegetation is quite dense [73]; and (ii) the low correlation between NDVI and water stress. NDVI commonly shows an asymptotic saturation in areas with high biomass indices [74]. These saturation effects can mask changes in vegetation dynamics and biophysical processes. In addition, the ability of NDVI to convey information about vegetation water content is limited, since the index utilizes wavelength related to internal leaf structure and to photosynthetic processes, and does not give a measure directly related to the quantity of water in the leaf and to vegetation water stress [75]. The quantity of water available in a leaf’s internal structure largely controls infrared short-wave (SWIR) wavelengths (between 1.2 and 2.6 μm) [76]. This limitation of NDVI in relation to water stress could be partly overcome by using vegetation indices that are more sensitive to canopy water availability and leaf water content or by incorporating the relation between soil moisture and surface resistance. One alternative is to use the normalized difference water index (NDWI) [77]. The combination of NIR with SWIR removes variations introduced by internal leaf structure and quantities of dry material, improving accuracy in monitoring water stress and giving a measure that is more indicative of water availability than NDVI [78–80]. Predicting turbulent fluxes of H constitutes the main step in SEBAL’s partition of energy, incorporating many of the uncertainties generated by the algorithm. The subjective choice of hot and cold pixels determines the accuracy of H and consequently LE, as shown by the high correlation between dT and LE. It is difficult to avoid this subjectivity in the selection of reference pixels. Allen et al. [1,81] suggest that the choice of warm pixels should be determined not from T_s alone, but also with reference to its relationships with other parameters, particularly vegetation indices like NDVI or LAI.

Estimation of daily ET requires the integration of instantaneous fluxes R_n, G and LE predicted by SEBAL using EF and R_n,24h. As a starting point, the accuracy of estimated EF was assessed relative to the measured data. Next, the validation of the EF as a constant indicator of energy partitioning throughout the day (taken as the period between 7:00 h and 18:00 h) was examined. When the estimated instantaneous EF was compared with observed values, an overestimation by 12% and 18% was found at USE and PDG sites, respectively, most probably as a consequence of underestimation of turbulent fluxes measured by the EC system and in SEBAL’s energy balance closure, causing significant reduction in EF (Figure 3(b)). Figure 5 shows estimates of instantaneous energy fluxes found using SEBAL and the daily energy cycle observed at EC monitoring sites for two days during wet and dry seasons, together with diurnal variability in EF at those sites.

When instantaneous data were converted to daily ET, the estimated seasonal variation in R_n,24h (Figure 6(a)) and ET_24h (Figure 6(b)) agreed, respectively, with in situ measurements. Estimated values of R_n,24h significantly explained over 85% of the variation of measured data ate USE site (r² = 0.85, p < 0.05) and at the PDG site (r² = 0.86, p < 0.05). R_n,24h was overestimated by about 23 W·m⁻² and 26 W·m⁻² at USE and PDG sites, since this method (based on Equation (6)) does not correct for the radiation losses observed throughout the day as a function of cloud cover and atmospheric aerosols. Furthermore, this sinoidal model reduces R_n to zero during the night-time when effectively R_n becomes negative. As R_n goes to zero, we are assuming that ET goes to zero as well. According to Fisher et al. [82] without large wet surfaces, night-time ET is minimal because both photosynthesis and transpiration approaches zero as radiation diminishes. Using this simple scheme to predict daily R_n we are trying to overcome the need for ground information as model input.

With regard to ET_24h derived from SEBAL, estimated values significantly explained between 66% and 76% of the variation of measured data at the USE site (r² = 0.76, p < 0.05) and at the PDG site (r² = 0.66, p < 005), respectively. At USE site, estimated ET_24h varied between 5.9 mm·day⁻¹ in the wet season and 1.2 mm·day⁻¹ in the dry season, whilst observed values varied from 5.0 mm·day⁻¹ to 1.5 mm·day⁻¹ in the wet and dry seasons. At PDG site, estimated ET varied from 6.6 mm·day⁻¹ in the wet season to 2.3 mm·day⁻¹ in the dry season, with observed values varying from 6.5 mm·day⁻¹ to 1.2 mm·day⁻¹ in wet and dry seasons. Estimated and observed values had similar standard deviations, but ET was overestimated by 0.8 mm·day⁻¹ at USE, and by 1.15 mm·day⁻¹ at PDG, on average, reflecting the overestimation of EF and R_n,24h.

After calibration and validation the MGB-IPH hydrological model, daily ET estimations were compared with ET measured by EC at the USE and PDG sites. PDG site was compared with HRU 4 (forest and reforested areas on soils with medium storage capacity) and the USE site with HRU 2 (cropland areas with soils of high storage capacity), lying in the same area as the flux towers. At the PDG site the average ET estimated by the MGB-IPH model was 2.5 ± 1.4 mm·day⁻¹, whilst the measured ET was 2.6 ± 1.2 mm·day⁻¹, with RMSE equal to 0.72 mm·day⁻¹ (Figure 7(a)). Average ET estimated by the MGB-IPH model at the USE site was 2.7 ± 1.1 mm·day⁻¹, while the EC-measured ET at the same site was 2.6 ± 1.1 mm·day⁻¹, with RMSE 0.51 mm·day⁻¹ (Figure 7(b)). Compared to measured data, estimated ET_24h significantly explained over 64% of the variation of measured data at the PDG site (r² = 0.64, p < 0.05) and at the USE site (r² = 0.67, p < 0.05). We also found that the MGB-IPH model overestimated ET at the USE site by about 0.06 mm·day⁻¹, and underestimated it by about 0.13 mm·day⁻¹ at the PDG site.

A crucial point in spatial modelling of the energy balance is the capacity of thermal images to distinguish patterns of land use and land cover, since T_s is one of the most important parameters for estimating ET, followed by soil moisture and the fraction of vegetation in each pixel [83]. The great advantage in using MODIS data for estimating ET is the high accuracy of surface temperature images [84,85] associated with the spatial variability of this process at the regional scale. Two analyses were made to validate ET at the basin scale: (i) average ET_24h estimated by SEBAL was compared with ET_24h estimated by MGB-IPH, in the overlay area for which the two models were applied (an area of about 38,100 km²), and (ii) average ET_24h estimated by the two models were compared for different land use and land cover types, taking the hydrological response units (HRU) in the MGB-IPH as the analytical classes.

Modelled mean ET_24h for the area of 38,100 km² explain over 88% of the variation observed in the MGB-IPH model (r² = 0.88, p < 0.05) (Figure 8) with a RMSE of 0.48 mm day⁻¹. The SEBAL overestimated ET_24h by about 0.45 mm·day⁻¹ when compared with the model MGB-IPH, a difference of 14%. In the wet season the overestimation was about 0.16 mm·day⁻¹; while during the dry season the overestimation was about 0.60 mm·day⁻¹. In the wet season the mean ET_24h from the MGB-IPH model was 4.6 ± 0.6 mm day⁻¹ in comparison to an average of 4.8 ± 0.6 mm day⁻¹ from the SEBAL model. In the dry season the mean ET_24h from the MGB-IPH model was 2.1 ± 0.8 mm·day⁻¹ in comparison to an average of 2.6 ± 0.8 mm·day⁻¹ from the SEBAL model. In both seasons, estimations of ET_24h from SEBAL were higher than those given by MGB-IPH, although the difference was greatest in the dry season, related to SEBAL overestimations of instantaneous LE, EF and R_n24h.

Land use and land cover in the Rio Grande basin is a complex mosaic of agricultural and natural areas. Of the six HRU’s used in MGB-IPH, the following four can be found in the overlay area: (1) pasture, fields and agricultural areas in areas of medium infiltration capacity, covering 22% of the area; (2) agricultural areas in soils with high infiltration capacity, covering 36% of the area; (4) forest and reforested areas on soils with medium infiltration capacity, 16% of area; (5) pasture, fields and bare soil where soil has high infiltration capacity, 25% of area. Although SEBAL overestimated ET_24h relative to MGB-IPH, correlations between the two models in the four HRU’s were moderate to high, significantly explaining from 46% to 86% of the variation of measured values. Correlation was higher for agricultural areas, fields and pastures on soils with medium and high infiltration capacity; in forested areas, it was lower than for other units (Table 1).

Differences between correlations may be mainly the consequence of the complex system of land use and land cover and of the different input data and parameterizations used by the two models. In the MGB-IPH, the estimate of ET is based mainly on meteorological data obtained from field stations. Surface parameters are adjusted to agree with existing land use and land cover maps. Thus the variation in time and space of vegetation parameters such as albedo, LAI and r_s is determined by average values given in the literature, which probably do not accurately describe the best spatial variation in vegetation. For example, HRU 2, covering an area of about 13,600 km² and characterized by different agricultural cultivation, uses the same surface parameters for all of them. By contrast, the more important input variables to SEBAL, such as NDVI, albedo and T_s more faithfully describe temporal and spatial vegetation processes, giving less attention to micrometeorological information which is difficult to obtain at a regional scale.