3.1 Climate models performance
The performance of GCMs in simulating ETo show under/overestimations that varied according to region and model (Figures 1 and 2). By contrast, the results using the Tu method (Figure 1) and the Ab method (Figure 2) were quite similar. The ensemble mean of GCMs smoothened the individual biases of the models, but still showed overestimations for some locations throughout the year, mainly in the North of Brazil (Figures 1 and 2).
There was divergence in ETo estimation among the GCMs when using Tu (Figure 1) and Ab (Figure 2) methods, different from results from Llopart et al. (2020) when using a combination of 2 global and 8 regional models for South America. The CanESM2, CNRM-CM5, IPSL-CM5A-MR and MIROC-ESM models showed overestimations (up to 2.5 mm day-1) in both methods, mainly in the North of Brazil, and in parts of the Center-West. The HadGEM2-CC and MRI-CGCM3 models showed underestimations (up to 1.5 mm day-1) in the Southern and Northeastern regions of Brazil, respectively. In general, both methods showed the same under/overestimates per region and per model. The only difference was that under/overestimates were more intense in the Ab method (Figure 2) than in the Tu method (Figure 1).
When individually analyzing model performance in simulating the variables that are used to calculate ETo, we identified that the temperature patterns (mean and maximum) were similar among the GCMs, except for CanESM2, which had overestimations up to 5°C for the northern region of Brazil during the austral spring (Supplementary Material 1 and 2). For RH (SM. 3), the CanESM2, CNRM-CM5 and IPSL-CM5A-MR models gave underestimates above 10%, mainly in the North, and overestimates from the Northeast to South of Brazil. The HadGEM2-CC, MIROC-ESM and MRI-CGCM3 models showed an opposite trend for under/overestimated, i.e., the models could not adequately simulate RH, showing discrepancies among the GCMs with respect to the data. The GCMs patterns diverged from each other mainly in the Rs simulations (SM. 4), with most overestimates (greater than 3 MJ m-2 day-1) for all of Brazil throughout the year. In general, the MRI-CGCM3 better represented the climate variables (in magnitude and spatial pattern), and consequently better represented ETo estimates (Figures 1 and 2). This result is different from Guimarães et al. (2016) performed for the Northeast of Brazil, where the HadGEM2-CC climate model performed the best for ETo (correlation = 0.6 to 0.8) of all the GCMs studied.
3.2 Climate changes on ETo
Figures 3 to 6 show the seasonal and annual climate changes projected for ETo using the Tu and Ab methods under different radiative forcing scenarios for the end of the 21st century (2071-2100) for all of Brazil. In general, climate change projections for ETo relative to RCP 4.5 (Figures 3 and 5) show similar spatial patterns with lower intensity compared to RCP 8.5 (Figures 4 and 6). Additionally, the projected climate changes for ETo show similar spatial patterns and magnitudes between the different estimation methods. The Tu method gave lower intensity results compared to the Ab method.
Both methods project a general increase (0.6 to 1 mm day-1) for ETo, mainly in the North, Northeast, and Center-West of Brazil for the CanESM2, HadGEM2-CC and MIROC-ESM models. The CNRM-CM5 and MRI-CGCM3 models showed less intense increases (0.2 to 0.4 mm day-1) for all of Brazil. The IPSL-CM5A-MR model had the smallest projected increases (0 to 0.2 mm day-1), mainly using the Tu method. Almost all of Brazil will be affected by increases greater than or equal to 1 mm day-1 in the ETo rate under greater radiative forcing scenarios (Figures 4 and 6). The climate projections by the ensemble mean for the six GCMs using the different estimation methods (Tu and Ab) showed a tendency for increased ETo for all of Brazil, but the magnitude of this increase was smoother, mainly in the North, Northeast, and Center-West of Brazil (Figures 3-6). These results corroborate the results of Cardoso and Justino (2014), who calculated ETo using the Penman-Monteith method for a regional climate model coupled with a potential vegetation model, and Llopart et al. (2020), who considered a simplified water balance with regional climate models. Both authors obtained an increase of up to 3 mm day-1 for the Northern region of Brazil. However, our results differ from Andrade et al. (2020), who used soil water assessment tools and regional climate models and obtained a reduction of 0.36 mm day-1 for a part of Northeastern Brazil.
The climate change projections for T, Tmax, RH and Rs for RCP 4.5 show similar spatial patterns, but with lower intensities than RCP 8.5. For brevity’s sake, the supplementary material shows projections for only these variables for scenario RCP 8.5 (SM. 5-8). The GCMs show good agreement among each other for T (SM. 5) and Tmax (SM. 6) projections, with increases towards the end of the 21st century up to 6°C for RCP 8.5. The most intense temperature changes (from 4 to 6°C) were projected in the CanESM2, HadGEM2-CC, IPSL-CM5A-MR and MIROC-ESM models, mainly for the North and Center-West regions of Brazil. The CNRM-CM5 and MRI-CGCM3 models projected less intense increases (from 2 to 3°C) for southern Brazil.
RH projections showed variable spatial patterns and magnitudes among the GCMs for all of Brazil (SM. 7). Nonetheless, generally these tended to decrease by 6% (RCP 4.5) to 10% (RCP 8.5) towards the end of the 21st century. This RH reduction can be explained by decreased precipitation across most of Brazil (Llopart et al. 2020; Sousa et al. 2019). In the South of Brazil, where precipitation increases are projected, there was no significant projection for increased/reduced RH. In the CanESM2, CNRM-CM5, HadGEM2-CC and MIROC-ESM models, the greatest RH reduction (~ 10%) occurred in the North and Center-West of Brazil projected throughout the year, and in the Northeast of Brazil during JJA and SON in the MRI-CGCM3 model. By contrast, the IPSL-CM5A-MR model did not show significant trends towards increased or decreased RH towards the end of the 21st century.
The Rs projections were different among the six GCMs (SM. 8). The CanESM2, HadGEM2-CC, MIROC-ESM and MRI-CGCM3 models projected increased Rs at around 3 MJ m-2 day-1, mainly in the North and Northeast of Brazil. The CNRM-CM5 model did not show any significant increase (or reduction) for the end of the 21st century. The IPSL-CM5A-MR model, on the other hand, showed a reduction at 1.5 MJ m-2 day-1 in the extreme North of Brazil, and inland in the Northeast. This pattern was also observed by Cardoso and Justino (2014), who explained these divergences as changes in surface albedo and in the heterogeneity of precipitation projections from the individual regional climate models.
In general, the results converge to the spatial and temporal patterns expected in the signal change (increase), since the projected increases in air temperature and reductions in relative humidity should lead to increased ETo (Lemos Filho et al. 2010; Santos et al. 2017; Jerszurki et al. 2019). With respect to spatial and temporal patterns, results released by the IPCC (2013, 2021), Torres and Marengo (2014) and Torres et al. (2021) proved that increases in temperature will be more intense in the North, Northeast and Center-West of Brazil, and there will be different precipitation pattern changes, which will be negative (positive) in the Northeast (South). This indicates greater ETo increases in the North, Northeast, and Center-West of Brazil, and possibly lesser increases in the South of Brazil, as demonstrated using both methods (Figures 3-6).
Some authors (e.g., Fan et al. 2016; Gao et al. 2017; Lin et al. 2018) emphasize that impacts to evapotranspiration arise from interactions between climatic factors and local conditions, e.g., type of vegetation cover, and the impacts of human activities. Such factors increase uncertainties with respect to the contribution that each variable, both above and below ground (Ruosteenoja et al. 2018; Monteiro et al. 2021), will have on evapotranspiration processes in future climate conditions. New analyses should be performed with recent state-of-the art GCMs (CMIP6), that have been evaluated in the IPCC Sixth Assessment Report (IPCC AR6), using different socioeconomic pathways (Eyring et al. 2016). Moreover, future studies could take into account additional important meteorological variables for impact evaluations, like soil moisture.