Catchment-balance ET provides the closest approximation to a direct ET “measurement” over large spatial scales in this study. Using this approach, ET is calculated as the difference between terms in the water-budget equation that can be measured (within a margin of error), following Eq. (1): 1ET=P-R-dSdt, where P is area-weighted, catchment-mean precipitation; R is river runoff from the basin; and dSdt is the area-weighted, basin-mean change in terrestrial water storage (S) over the basin with respect to time (t), all in units of mm per month. Catchment-balance ET was calculated, first as the simple difference between precipitation and runoff (climatological basin means only) and then using the more sophisticated approach that accounts for temporal variation in groundwater storage (Rodell et al., 2011; Long et al., 2014; Swann and Koven, 2017; Maeda et al., 2017; Sun et al., 2019).

The catchment-balance approach was used to estimate climatological annual mean ET for the Amazon Basin and 10 sub-catchments: the Solimões, Japurá, Negro, Branco, Jari, Purus, Madeira, Aripuanã, Tapajós. and Xingu catchments (Fig. 1). Temporal variation in catchment ET was analysed for the Amazon Basin only. Basin domains were constructed by aggregating sub-basin shapefiles that had previously been identified using a digital elevation model (Seyler et al., 2009), making sure to include all sub-basins upstream of the relevant river station.

Precipitation data came from the 0.05∘×0.05∘ Climate Hazards Group InfraRed Precipitation with Station (CHIRPS) version 2.0 dataset, which combines data from satellites and rain gauges (Funk et al., 2015). CHIRPS has been validated against rain-gauge data from northeast Brazil, including four Amazon stations, and has been found to have mean bias and absolute error values of -3.6 % and 28.4 mm per month respectively (Paredes-Trejo et al., 2017).

Monthly mean river flow data were obtained from the Agência Nacional de Águas (ANA) database in Brazil (HidroWeb, 2018). To obtain runoff in millimetres per month, volumetric flow rates (m3 s-1) were divided by the catchment area (m2), scaled to the monthly time step by multiplying by the number of seconds in each month and multiplied by 1000 to convert to millimetres. To estimate “whole” Amazon ET, we used runoff measured at Óbidos, which drains approximately 77 % (Callède et al., 2008) of the Amazon Basin (Fig. 1). For the Tapajós catchment, runoff from Itaituba was gap-filled based on linear regression with data from the Buburé station, which is approximately 70 km upstream (R2=0.77, 15 data points in total). Details of the gauge stations used for the other basin river records are provided in Table S1 in the Supplement.

Terrestrial water storage data were derived from the 0.5∘×0.5∘ Jet Propulsion Laboratory (JPL) RL06M Version 2.0 GRACE mascon solution, with coastline resolution improvement (CRI) filtering and land-grid scaling factors (derived from the Community Land Model, CLM) applied (Watkins et al., 2015; Wiese et al., 2016, 2019). This dataset, which has been processed to minimise measurement errors and optimise the signal-to-noise ratio, represents a new generation of GRACE solutions that do not require empirical post-processing to remove correlated errors and are, thus, considered to be more rigorous than the previous GRACE land water storage estimates based on spherical-harmonic solutions (Wiese et al., 2016).

To determine the change in water storage dSdt, in units of millimetres per month, we calculated the difference between consecutive GRACE measurements for each grid cell, divided by the time between measurements, as shown in Eq. (2): 2dSdt=S[n]-S[n-1]/dt, where S represents the land water storage anomaly (in mm), n is the measurement number, and dt is the time between measurements [n] and [n-1] in months. Following this, we calculated the area-weighted, basin-mean dSdt for each catchment. Finally, to account for the uneven temporal sampling of GRACE data (due to battery management on the GRACE satellites), we used a linear spline to interpolate dSdt values to the same temporal grid as the precipitation and runoff data, i.e. one value per month for the period from May 2002 to December 2019.

Previous work has shown that GRACE is less sensitive at lower latitudes than at higher latitudes and may only be capable of detecting monthly changes in groundwater storage over regions larger than 200 000 km2 or seasonal changes over areas greater than 184 000 km2 (Rodell and Famiglietti, 1999). Three of the basins included in this analysis have areas smaller than these thresholds, namely Jari (49 000 km2), Branco (131 000 km2), and Aripuanã (138 000 km2, Table S1). However, we only computed climatological means over these basins, and the catchment-balance ET estimates were in excellent agreement with ET calculated as the difference between precipitation and runoff (r=0.997, p<0.001; Fig. S1 in the Supplement). Therefore, we have confidence that our results for these basins were not biased by the inclusion of GRACE in the calculations.

For the Amazon Basin only, we calculated catchment-balance ET at the monthly timescale. We estimated the relative uncertainty of our ET estimates (υET) by propagating errors in each of the terms of the water-budget equation (Rodell et al., 2011), following Eq. (3): 3υET=σP2+σR2+σdSdt2ET, where σP, σR, and σdSdt represent the absolute uncertainties in P, R, and dSdt respectively. Errors in precipitation were estimated as the random error (σP_random) plus the systematic error (σP_bias), combined in quadrature. Random errors were calculated following Eq. (4), from Huffman (1997): 4σP_random=r‾H-ppN12, where r‾ is the climatological mean precipitation over the basin, H is a constant (1.5), p is the frequency of non-zero rainfall, and N is the number of independent precipitation samples (defined as the number of Amazon pixels with finite P measurements in each month). For σP_bias, we used the value of -3.6 % estimated for CHIRPS from a validation analysis based on data from 21 meteorological stations in northeast Brazil (Table 4 in Paredes-Trejo et al., 2017). σR was estimated as 5 % of monthly river flow (Dingman, 2015). Uncertainty in groundwater storage was quantified by combining GRACE measurement errors and leakage errors (residual errors after filtering and rescaling) in quadrature. For these, we used Amazon-specific values from the literature (6.1 and 0.9 mm for measurement and leakage errors respectively) that had been calculated after CRI filtering and CLM scaling factors had been applied (Table 1 in Wiese et al., 2016). Finally, as dSdt values were calculated using data from two consecutive months, groundwater error values were multiplied by 2 to obtain σdSdt (e.g. Maeda et al., 2017). We calculated a mean υET value of 16.1 % (standard deviation =9.2 %) for Amazon catchment-balance ET (Fig. S2). At the monthly timescale, the dSdt and precipitation terms were found to be the dominant sources of uncertainty (σdSdt=8.7 mm, σP=6.8 mm), followed by runoff (σR=4.9 mm; Table S2). Seasonal and interannual time series of precipitation, runoff, dSdt and ET, and their associated errors, are shown in Figs. S3 and S4. Due to small interannual variation in dSdt (Fig. S4), climatological estimates of ET calculated with and without water storage estimates were similar (Figs. 1, 2). Data from August 2017 to June 2018 were removed due to anomalously low and possibly unreliable dSdt data over this period (Fig. S4c). We tested the sensitivity of our interannual trend analysis to the removal of these data points and found it had no statistically significant impact on the reported results.

Three global, satellite-derived ET products and one reanalysis dataset were included in this study. The Moderate Resolution Imaging Spectroradiometer (MODIS) MOD16A2 Version 6 ET product (Mu et al., 2011, 2013; Running et al., 2019) was downloaded at a 500 m resolution from the NASA Earth Data website (https://earthdata.nasa.gov, last access: June 2020) for the period from 2001 to 2019. The MODIS ET algorithm is based on the Penman–Monteith equation (Monteith, 1965), which uses temperature, wind speed, relative humidity, and radiation data to approximate net ET, but it is modified by scaling canopy conductance by LAI. The sinusoidal 500 m MODIS tiles were merged and reprojected to a regular latitude–longitude grid (WGS84), using the Geospatial Data Abstraction Library software (GDAL/OGR Contributors, 2020) and resampling via weighted averaging. We also obtained ET estimates from the 8 km Process-based Land Surface ET/Heat Fluxes algorithm (P-LSH) product provided by the Numerical Terradynamic Simulation Group at the University of Montana (Zhang et al., 2010, 2015b) for the period from 1982 to 2013. This ET product is also based on the Penman–Monteith equation but uses an algorithm that incorporates remote-sensing normalised difference vegetation index (NDVI) data to estimate canopy conductance. Additionally, ET were retrieved from the satellite-constrained Global Land Evaporation Amsterdam Model (GLEAM) v3.3b dataset (Martens et al., 2017; Miralles et al., 2011) at 0.25∘×0.25∘. This version of GLEAM is based on satellite data only and is available for the 2003–2018 period. GLEAM is based on the Priestley–Taylor framework (Priestley and Taylor, 1972), which uses temperature and radiation to estimate potential ET (PET) and a hydrological model to convert PET to actual ET. Finally, 0.25∘×0.25∘ ET data were retrieved for the 2001–2019 period from the European Centre for Medium-Range Weather Forecasts ERA5 reanalysis, which incorporates observations into a model to provide a numerical description of historical climate (Hersbach et al., 2020). As ET is not among the many observations that are assimilated in the reanalysis, ERA5 ET is independent of the other ET datasets analysed in this study. To permit a meaningful comparison between datasets, all satellite and reanalysis ET products were re-gridded to 0.25∘, analysed at a monthly timescale, and averaged over the common time period from 2003 to 2013 for those analyses based on temporal means. A summary of the equations and datasets used to derive the satellite ET products is presented in Table 1.

We obtained historical simulations of ET from models participating in CMIP5 and CMIP6 for the 1994–2004 and 2001–2014 periods respectively. We selected models that also provided precipitation, surface shortwave radiation, and LAI output, in order to investigate model processes controlling ET. In total, we used data from 13 CMIP5 models and 10 CMIP6 models (Tables S5, S6). Output was downloaded at a monthly resolution from the Centre for Environmental Data Analysis archives (http://archive.ceda.ac.uk, last access: August 2020), accessed via the JASMIN supercomputer. Where available, multiple realisations were used to derive an ensemble mean for each model, otherwise a single run was used. For basin-scale ET estimates, annual and seasonal climatological means were calculated for each model separately, using native-resolution data (see Tables S5 and S6), and then subsequently averaged across models. For CMIP5, climatologies were computed using data from 1994 to 2004 (the most recent 11 years of available data), whereas CMIP6 climatologies were estimated using the same period as for observations (i.e. 2003–2013). To visualise the spatial variation in ET over the Amazon and make comparisons with site-level ET measurements, multi-model ensemble means were also computed for CMIP5 and CMIP6. To do this, we re-gridded ET from each model to the same 1∘×1∘ horizontal grid and then calculated the ensemble mean across all models. Although not all models simulate the level of detail provided by a 1∘×1∘ grid (see Tables S5 and S6 for native resolutions), this resolution enabled us to extract data from each Amazon sub-basin with more accuracy than using a coarser grid.

We compared differences in ET magnitude, spatial variation, seasonality, and trends over the past 2 decades, identifying where estimates were in good agreement and where inconsistencies occurred. For annual comparisons, we computed climatological means over the Amazon Basin (the area drained by Óbidos; Fig. 2) and its sub-catchments (Fig. 3), using an area-weighted averaging approach. We applied a two-sample Kolmogorov–Smirnov test (Hodges, 1958) to identify whether monthly Amazon ET values from 2003 to 2013 from satellite, reanalysis, and climate models were drawn from the same distribution as the catchment-balance ET values. We examined how well each ET product was able to capture spatial variation in Amazon ET, using comparisons with catchment-balance ET estimates and flux tower measurements and by correlating basin-scale annual means with catchment-balance ET (Table S7). ET products were also evaluated at the seasonal timescale over the Amazon catchment and at the K34 flux tower site (Fig. 1). For comparisons between flux tower and gridded ET data, we selected data from the single grid cell containing the tower.

All data were analysed over the 2003–2013 period with the exception of CMIP5, which was analysed over the 1994–2004 period. The Amazon hydrological cycle has intensified between these periods, with increases in basin-mean P (Gloor et al., 2013); therefore, we might expect CMIP5 ET to show some differences from other ET products. However, results from CMIP5 were largely consistent with results from CMIP6, showing that any differences caused by the analysis time period were smaller than the differences between the models and other types of ET data. We acknowledge that the period for evaluating Amazon ET is relatively short, although we were constrained by our reliance on satellite data and the availability of climate model output.

We also analysed linear trends in Amazon Basin ET, using data averaged across all months (annual), the wettest 3 months (January–March, JFM), and the driest 3 months (July–September, JAS) over the past 2 decades using ordinary least squares regression. Years with fewer than 10 months of data were excluded from the annual time series (2017 and 2018), and years with any missing months in JFM or JAS were excluded from the wet and dry season time series (2017 in JAS only). Trends were analysed over the time period common to all datasets (2003–2013) and across all years with available data for each dataset.

To better understand differences between ET products, we analysed relationships with potential drivers of ET, including precipitation, surface radiation, and LAI. Satellite-based ET estimates were compared with precipitation from CHIRPS, radiation from CLARA-A1 (CLoud, Albedo and RAdiation dataset, AVHRR-based, version 1; Karlsson et al., 2013), and LAI from the quality-controlled MODIS MOD15A2H Collection 6 (C6) product provided by Boston University (Myneni et al., 2015; Yan et al., 2016a), which were all re-gridded to 0.25∘×0.25∘. MODIS LAI has been shown to perform relatively well against ground-based LAI measurements (R2=0.7–0.77), although uncertainty regarding the validity of high LAI values (>4 m2 m-2), such as those that occur over the Amazon, is larger due to there being few ground measurements and the satellite reflectance signal reaching saturation over dense canopies (Yan et al., 2016b). Furthermore, the satellite-based MODIS ET product incorporates MODIS LAI (Table 1); thus, these datasets are not fully independent of one another. CLARA-A1 radiation is independent of the ET datasets evaluated in this study and is estimated to have an accuracy of ≤10 W m-2, although few validation measurements were available over South America and none were available in the Amazon region (Karlsson et al., 2013). Thus, there is some uncertainty in the accuracy of these satellite products over the Amazon that must be considered when interpreting the results. Reanalysis and model ET were compared with reanalysis and model variables respectively. For ERA5, we used the “high vegetation” LAI field as the Amazon is predominantly covered with tropical forest, although repeating the analysis with “low vegetation” LAI made little difference to the results. For the K34 tower site, ET was compared against precipitation and radiation data only. Half-hourly measurements of precipitation and incoming radiation from the tower site were averaged and scaled to a monthly resolution, following the same procedures as applied to the ET data. Due to missing data in several years, climatological means and seasonal cycles for K34 were calculated using all data from 1999 to 2017.

We analysed controls on spatial variation in ET by comparing catchment-mean values against catchment means of precipitation, radiation, and LAI. As there were only 11 data points in this analysis (representing the Amazon and 10 sub-catchments), we also analysed the response of ET to spatial variation in its potential drivers at the grid-cell level, following a similar approach to Ahlström et al. (2017). This enabled us to better understand non-linear relationships between ET and its controlling variables. Mean annual ET values from all Amazon grid cells were binned by annual precipitation, radiation, and LAI using bin widths of 100 mm  yr-1, 5 W m-2, and 0.2 m2 m-2 respectively. Bins with fewer than five data points were excluded from the analysis. Finally, to distinguish between the controls on seasonal variation in ET from the controls in interannual variation in ET, we analysed relationships between ET and possible driving variables at the climatological monthly timescale and at the interannual timescale. While this approach was useful to understand the relative importance of controlling variables at different timescales, it reduced the number of data points in each analysis such that statistical power was correspondingly low. This meant that when we did not detect a statistically significant signal then it could either be because there was no signal to detect or because the signal-to-noise ratio was too low. This should be taken into consideration when assessing the analysis of controls on Amazon ET reported here.

Climatological annual Amazon ET estimates from water-balance approaches, satellite-based products, reanalysis, and two coupled-model ensembles are presented in Fig. 2. ET from catchment balance was the lowest of all estimates (mean ± standard deviation =1083±37 mm yr-1 for 2003–2013; Fig. 2, Table S7), which, given uncertainties, is indistinguishable from the value obtained from differencing precipitation and runoff (1102±53 mm yr-1). This confirms that the GRACE-observed changes in groundwater storage are relatively small over decadal timescales. Our mean annual catchment-balance ET estimate for the Amazon was very similar to that from a previous catchment-balance study (1058 mm yr-1), calculated over the same drainage region (drained by Óbidos) but based on different precipitation data and an alternative GRACE solution (Swann and Koven, 2017), suggesting that the approach is relatively robust. The area drained by Óbidos excludes the far eastern Amazon, which our spatial catchment-balance analysis revealed to have the highest annual ET across the basin, decreasing towards the west and south (Fig. 3a, b). This may explain why our catchment-balance annual Amazon ET value was towards the lower end of previous estimates (Marengo, 2006).

Annual Amazon ET from satellites, reanalysis, and coupled models was 15 %–37 % higher than catchment-balance ET, with GLEAM showing the largest bias (Fig. 2). With the exception of GLEAM, mean annual ET values from satellites, reanalysis, and coupled models were remarkably similar to one another (within 50 mm, or <4 %), with a mean bias of 18 % (relative to catchment-balance ET). ET from all of the products and models analysed showed statistically different distributions from catchment-balance ET (Kolmogorov–Smirnov test; Fig. S5a), tending to show a narrower range and fewer low ET values (Fig. S5b). This substantial and consistent overestimation of annual Amazon ET across data products and coupled models highlights that even basic features of the Amazon hydrological cycle are still not well characterised.

MODIS and P-LSH captured a northeast to southwest gradient in ET across the basin that was evident in the water-balance approaches, showing the highest ET over the Guiana Shield in the north of the Amazon and decreasing southwest across the basin (Fig. 3c, d). Catchment-mean ET values from these two products were strongly correlated with ET from the catchment-balance approach across the 11 basins analysed in this study (r=0.84, p<0.01 and r=0.82, p<0.01 for MODIS and P-LSH respectively), although spatial variability was weaker and interannual variability was also strongly underestimated (Fig. S7, Tables 2 and S7). Flux tower ET measurements, although spatially limited, appear to show an east–west gradient in Amazon ET, with the highest annual values over forest and seasonally flooded sites in the east of the basin (coloured circles in Fig. 3). However, the gradient in tower data should be interpreted with some caution, as variation in energy-balance closure between sites will affect the absolute ET values (da Rocha et al., 2009a; Fisher et al., 2009). Furthermore, two nearby towers in the northeast Amazon showed a clear difference in mean annual ET (K67 and K83), likely due to being located on different land-cover types (primary forest and selectively logged forest respectively; Table S5). ET from GLEAM, which exceeded 1400 mm yr-1 over much of the Amazon, showed a north–south ET gradient (Fig. 3e, see Fig. S6 for an alternative scale) and a positive, although not statistically significant, correlation with catchment-balance estimates (r=0.51, p=0.11; Fig. S7, Table S7). Previous studies based on flux tower measurements (Fisher et al., 2009), water-budget analysis (Zeng et al., 2012; Maeda et al., 2017; Sun et al., 2019), and a combination of satellites and flux towers (Paca et al., 2019) showed similar north/northeast–south/southwest gradients in ET across the Amazon, in line with the catchment-balance results presented in Fig. 3.

ET from ERA5, CMIP5, and CMIP6 bore no relation to catchment-balance ET, simulating the highest ET values in the northwest of the basin and decreasing to the east (Fig. 3e–g). The CMIP models do not incorporate any observations and, therefore, might not be expected to perform as well as the other products analysed in this study. However, an analysis of Amazon precipitation in 11 CMIP5 models found that most were able to capture spatial patterns relatively well, including shifting distributions through the course of the seasonal cycle (Yin et al., 2013). The poor representation of spatial variation in Amazon ET in reanalysis and coupled models shown in Fig. 3 demonstrates a need for improvement of this key hydrological variable in these products.

To understand the drivers of spatial variation in Amazon ET, we compared catchment-scale estimates against catchment means of precipitation, surface radiation, and LAI (Fig. 4). As there were only 11 data points in the analysis (representing the Amazon and 10 sub-catchments), statistical power was relatively low. However, we found that spatial variation in catchment-balance ET showed some indication of an influence from radiation (r=0.38, p=0.25; Fig. 4h) but not from precipitation (r=0.14, p=0.68; Fig. 4a) or LAI (r=0.06, p=0.87; Fig. 4o). This result tentatively suggests that spatial variation in radiation explains more of the spatial variability in ET across Amazon sub-catchments than other variables. None of the ET products and models analysed captured positive relationships between catchment-mean ET and radiation. ET from ERA5 and the CMIP ensembles instead showed negative associations with radiation (Fig. 4l–n) and, along with GLEAM ET, positive relationships with precipitation (Fig. 4d–g), indicative of water availability influencing the spatial variation in ET (Fig. 4d–g). These results confirm that the reanalysis and climate models analysed here struggled to capture spatial patterns in Amazon ET due to misrepresentation of the controlling drivers, specifically the relative importance of precipitation and net radiation. ET from ERA5 and the models also showed positive correlations between LAI and ET (Fig. 4s–u), which are not seen in the satellite observations. However, it should be noted that satellite LAI was generally slightly lower and showed less spatial variability than other LAI datasets over the Amazon (Fig. S8i–l), likely due to the satellite sensor being insensitive to variation in LAI over areas of dense tropical forest (Yan et al., 2016b; Myneni et al., 2002). This could hamper our ability to accurately assess the extent to which LAI influences spatial variation in ET.

For further insights into the validity of Amazon ET products and the factors controlling ET, we evaluated ET responses to spatial variation in precipitation, radiation, and LAI at the grid-cell level (Fig. 5). Differences between ET products were most apparent in their responses to annual precipitation (Fig. 5a). Above 2000 mm yr-1, datasets followed three patterns of behaviour: GLEAM ET continued to increase to approximately 1600 mm yr-1; ET from MODIS, P-LSH, and ERA5 remained relatively stable at around 1300 mm yr-1; and CMIP5 and CMIP6 showed slight reductions in ET with further increases in precipitation. The precipitation threshold of 2000 mm yr-1 has previously been suggested as the level above which tropical forests are able to sustain photosynthesis during the dry season (Guan et al., 2015) and as the breaking point between productivity in the Amazon being water (<2000 mm yr-1) or radiation (>2000 mm yr-1) limited (Ahlström et al., 2017). Indeed, below 2000 mm yr-1 ET increased with increasing precipitation for all satellite, reanalysis, and model datasets (lines in Fig. 5a), indicating a water limitation on ET. The two catchments in the northwest Amazon where P exceeds 3000 mm yr-1, Japurá and Negro, were most closely aligned with the products that showed ET levelling off when precipitation exceeded 2000 mm yr-1 (i.e. MODIS, P-LSH, and ERA5), suggesting that these products represent the ET response to rainfall in very wet areas relatively well. For MODIS and P-LSH, this finding provides additional support that spatial patterns in Amazon ET correspond well with spatial variation in its controlling variables. In contrast, although ERA5 generally captured the correct ET response to precipitation (Fig. 5a), there are spatial differences between satellite and ERA5 precipitation datasets in Amazon regions with rainfall above 2000 mm yr-1 (Fig. S8a–d). This explains why relationships between ERA5 precipitation and ET differed at the catchment (Fig. 4e) and the grid-cell (Fig. 5a) scales. In the GLEAM model, the “stress factor” that is used to scale PET takes precipitation as an input variable to the soil module (Table 1), which, in turn, controls the amount of water available for ET (Martens et al., 2017). Our results indicate that the GLEAM model overestimates the dependence of ET on soil moisture in regions with high annual rainfall, highlighting a possible target for improvements to the GLEAM algorithm.

Differences between ET products in their relationships with other variables were more subtle. ET dependence on radiation was broadly similar among datasets, showing a peak at approximately 200 W m-2 (Fig. 5b). This is consistent with low and high levels of radiation tending to correspond to high and low levels of precipitation respectively (Fig. S8a–h) and ET peaking at an optimum between the two. LAI–ET relationships were also fairly consistent, with ET increasing relatively linearly with increasing LAI (Fig. 5c). GLEAM generally tended to overestimate ET relative to LAI, whereas CMIP5 underpredicted ET for a given LAI value, in comparison with ET from other products and catchment-balance estimates. In general, radiation over the Amazon was substantially higher in the models compared with satellite and reanalysis datasets (Fig. S8a–h), and satellite-derived LAI values were uniformly lower than other estimates (Fig. S8a–h), likely due to signal saturation (Myneni et al., 2007).

The mean seasonal cycle in Amazon ET was estimated from catchment-balance analysis, satellite, reanalysis, and model ET datasets for the whole Amazon Basin (Fig. 6). Amazon catchment-balance ET showed a strong seasonal cycle (standard deviation, σ=22 mm per month), with annual minima during April–June and maxima in August–October (Fig. 6). ET at the K34 tower site, located in the central Amazon, showed a similar seasonal pattern to that over the wider basin (Fig. S9), although intra-annual variation was weaker (σ=14 mm per month). Furthermore, we observed strong, positive correlations between ET and radiation for the Amazon Basin and the K34 tower site (r=0.93, p<0.001 and r=0.68, p<0.05 respectively; Figs. 7h, S10) as well as between ET and LAI for the basin (r=0.63, p<0.05; Figs. 7o, S11). These results agree with findings from da Rocha et al. (2009a), who made a detailed comparison of seasonal ET at seven flux tower sites in Brazil. They showed that ET increased during the dry season at the four wet tropical forest sites (including K34), contrasting with three transition-forest and savanna sites where ET followed seasonal soil moisture availability. The seasonal cycle in ET shown in Fig. 6 is consistent with studies reporting an increase in leaf flush driving Amazon greening in the dry season (Lopes et al., 2016; Saleska et al., 2016). Studies based on catchment-balance analysis (Swann and Koven, 2017), and satellite observations of vegetation photosynthetic properties (Guan et al., 2015) also showed that ET and forest productivity peak during the drier part of the year over the majority of the Amazon. Finally, our results are in agreement with those from Fisher et al. (2009), who identified radiation and NDVI as the primary and secondary controls on ET across the tropics based on analysis of flux tower measurements.

Monthly ET cycles from MODIS, P-LSH, and ERA5 correlated with Amazon catchment ET (r=0.61–0.67, p<0.05; Table 2, Fig. 6) and captured positive relationships with surface radiation (r=0.66–0.78, p<0.05; Fig. 7). However, despite representing the direction of seasonal fluctuations relatively well, these datasets underestimated the seasonal variability by 39 %–77 %, relative to catchment-balance ET (Fig. 6). Biases from catchment-balance ET were generally strongly positive from January to June and weakly negative in September and October. At K34, MODIS and ERA5 overestimated the seasonal ET range by 61 % and 28 % respectively, whereas P-LSH underestimated the range by 26 % (Fig. S9). With such poor representation of the magnitude of seasonal variability, and inconsistencies in the direction of amplitude biases, ET from these satellite and reanalysis datasets may be of limited use for assessing long-term changes in the seasonality of the Amazon hydrological cycle (Gloor et al., 2013) or for evaluating seasonal ET representation in coupled climate models.

ET from GLEAM, CMIP5, and CMIP6 neither correlated with seasonal catchment-balance Amazon ET nor captured the correct seasonal amplitude (Figs. 6, 7, Table 2). Instead, ET from these datasets followed the same seasonal cycle as precipitation, peaking during the wettest part of the year. A previous study comparing Amazon ET estimates derived using different methods also observed that climate model and reanalysis ET tended to follow the precipitation seasonal cycle, with annual ET minima in the dry season (Werth and Avissar, 2004). The authors suggested that this was due to a strong vegetation control on modelled ET due to downregulation of stomatal conductance in the dry season, concluding such a control to be as credible as a radiation control on Amazon ET. However, a subsequent study queried this assertion, citing evidence from flux towers as proof that vegetation controls on Amazon ET were secondary to environmental controls (Costa et al., 2004). Over the Congo, where ET follows the same seasonal cycle as precipitation, CMIP5 models were shown to capture the seasonality of ET but to overestimate the magnitude of the flux, particularly during the two wet seasons (Crowhurst et al., 2020). The results presented in Fig. 6 indicate a disconnect between our mechanistic understanding of the controls on seasonal Amazon ET based on catchment-balance analysis, and the algorithms used to predict ET in GLEAM and the CMIP models.

Northern and southern Amazon sub-basins were analysed separately, due to differences in the timing of the seasonal precipitation cycle above and below the Equator. Uncertainties in monthly ET estimates were higher over these areas than over the whole Amazon, although it was still possible to detect differences between catchment-balance ET and other datasets (Fig. S12). The seasonal cycle in catchment-balance ET was weaker in the north than in the south (σ=16 and 26 mm per month respectively), following the pattern of precipitation seasonality (σ=69 and 115 mm per month in northern and southern basins respectively). In general, satellite, reanalysis, and climate model ET related fairly well to seasonal catchment-balance ET in the northern Amazon (Fig. S12b) but showed much weaker relationships in the southern Amazon (Fig. S12c). The CMIP5 and CMIP6 models, which were unable to capture seasonal ET variation over the whole Amazon or southern Amazon, replicated month-to-month variation in ET over the northern Amazon well, although both model groups underestimated seasonal variability (Figs. 6, S12). MODIS, which captured seasonal ET over the whole Amazon (Fig. 6), performed especially poorly in the south, showing a negative relationship with catchment-balance ET (r=-0.57, p=0.06; Fig. S12b). These results suggest the ability of ET products to capture seasonal ET varies regionally, and a product that performs well over one region may not be reliable elsewhere. Finally, we note that relative uncertainties in ET estimated using the catchment-balance approach increase at smaller spatial scales, precluding a more in-depth assessment of seasonal ET over individual sub-basins.

Interannual time series of Amazon ET from 2001 to 2019 for the whole year, the three wettest months (JFM, see Fig. S10), and the three driest months (JAS) are shown in Fig. 8. From 2003 to 2013, interannual variability (σ) in catchment-balance ET was 2.9 mm per month, or 3.2 % of the climatological mean. This value is comparable to the interannual variation in precipitation over the same period (σ=3.6 %), half the variation in runoff (σ=7.0 %), and represents around 10 % of the seasonal variation in Amazon ET (Fig. 6). With only a relatively short time series, controls on interannual variability were hard to detect, although radiation appeared to play a role (Fig. S13). Interannual variation was underestimated in ET from satellites, reanalysis, and climate models by up to a factor of 6 relative to catchment balance (Fig. 8a, Table 2). In JFM and JAS, ET variation was higher than at the annual scale (catchment balance σ=8.89 and 8.91 mm per month respectively) and similarly underestimated by other datasets (Fig. 8b, c, Table 2). Relationships between interannual catchment-balance ET and ET from satellites or reanalysis were generally poor (Table 2), and an especially high JFM catchment-balance ET recorded in 2016, coinciding with a severe El Niño event (Koren et al., 2018), was not captured by other ET products (Fig. 8b). ERA5 and CMIP6 showed the least interannual variation, indicating poor model representation of the factors influencing inter-year changes in ET.

Finally, we assessed interannual trends in Amazon ET over the common time period of 2003 to 2013 and using all years of available data for each dataset (Table 3). No statistically significant temporal trends were observed for annual, JFM, or JAS catchment-balance ET over the respective periods analysed. Removal of the anomalous El Niño year had no impact on the results. Previous studies based on the P-LSH satellite product (Zhang et al., 2015b), and other satellite ET products and machine-learning approaches (Y. Zhang et al., 2016; Pan et al., 2020) have reported multi-decadal increases in ET, globally and over the Amazon, from the early 1980s to the early 2010s, due to long-term warming driving increased evaporative demand. Meanwhile, climate models predict that Amazon ET will decrease over the next century due to reductions in plant stomatal conductance driven by rising atmospheric CO2 (i.e. the CO2 fertilisation effect), leading to declines in Amazon rainfall (Skinner et al., 2017; Kooperman et al., 2018; Langenbrunner et al., 2019). Swann and Koven (2017) observed a statistically significant reduction in monthly catchment-balance Amazon ET from 2002 to 2016 (-0.12 mm per month yr-1), which they hypothesised may have been driven by a reduction in Amazon precipitation, deforestation, or CO2 fertilisation. Our catchment-balance ET data, analysed over a similar period but at the annual timescale, gave a similar value (i.e. -0.09 mm per month yr-1, 2003–2013; Table 3), although the result was not statistically significant due to the short length of the time series. Extension of the record to 2019 gave a similar result (Table 3). The absence of a discernible trend in catchment-balance ET in this study suggests that previously reported positive trends in Amazon ET may have levelled off but that there has not yet been a systematic shift towards long-term reductions in ET driven by precipitation, deforestation, or the CO2 fertilisation effect, over the portion of the Amazon drained by Óbidos (Fig. 1), with the caveat that ET changes over the eastern portion of the basin would not be detected in our approach.

Among other datasets, there was little agreement in the direction of ET trends, with both positive and negative trends detected at the annual timescale (P-LSH and MODIS respectively), and only one product showing a statistically significant upward trend in JAS ET (P-LSH; Table 3). There was more agreement in JFM, with MODIS, GLEAM, and ERA5 all showing modest declines in ET (-0.27 to -1.3 mm per month yr-1, variable time periods; Table 3). Divergent trends in remote-sensing ET products have been reported previously (Wu et al., 2020). Trends in satellite-derived climate datasets can occur from gradual changes in the satellite orbit over time (drift), which could explain some of the observed trend disparities, although such artefacts should have been corrected for during data processing (Gutman, 1999; Pinzón et al., 2005). Overall, the inconsistencies between satellite, reanalysis, and climate model ET records at the interannual timescale, and poor correspondence with catchment-balance ET, highlight that current products are inadequate for evaluating long-term changes in Amazon ET.