Robust Amazon precipitation projections in climate models that capture realistic land–atmosphere interactions

We obtained global observations of P and ET for an 11 year period (2003–2013). We used a merged satellite-gauge P product (Huffman et al 2007) and seven ET products, including three satellite-based datasets, three datasets based on interpolated flux-tower measurements, and a novel reanalysis, to overcome uncertainty in ET over the Amazon (Sörensson and Ruscica 2018, Baker et al 2021b). In addition to P and ET, we also analysed cloud cover (CLD), surface radiation (RDN) and soil moisture (SM) to examine model representation of physical processes along the full hydrological pathway. Details of all observational products are provided in table 1, with additional information in the supplementary methods.

Historical simulations from 38 CMIP5 models (supplementary tables 1 and 2) were downloaded at monthly resolution from the Centre for Environmental Data Analysis archive (http://data.ceda.acuk/badc/cmip5/). When available, multiple realisations were used to derive an ensemble mean, else a single run was used. We used data over an 11 year period (1994–2004) to align with observations. There is a discrepancy in the time periods analysed for models and observations (2003–2013). Although land–atmosphere interactions may be expected to evolve over time, as the two periods are separated by less than a decade we do not expect this to have had a substantial impact on our findings. All model simulations and observations were regridded to 1° × 1° resolution using an area-weighted approach to ensure an equal number of Amazon grid cells across datasets.

Simultaneous linear P-ET correlations were used to categorise controls on Amazon ET in observations and models. These correlations are not expected to capture the full complexity of land–atmosphere interactions over the Amazon, but rather to provide a broad indication of the direction of influence between the land surface and the atmosphere. Pearson correlation coefficients were computed between monthly anomalies of P and ET globally at the grid-cell scale for all datasets. Anomalies represent the deviation from the climatological mean and were derived by subtracting the long-term seasonal cycle from the monthly data. To constrain our analysis, we downloaded an Amazon basin shapefile (black boundary shown in figure 1) from observation service SO HYBAM (www.ore-hybam.org) and generated a 1° × 1° mask to identify Amazon grid cells. Datasets were only categorised if at least 25% of Amazon grid cells showed significant P-ET correlations. A t-test was used to identify whether the calculated coefficient was statistically different from zero and any dataset that did not meet this criterion was excluded from the study (1 CMIP5 model). To avoid overstating the significance of our results as a result of multiple-hypothesis testing, we applied a method to control for the false discovery rate, as suggested by Wilks (2016). We used the Benjamini/Hochberg approach (Benjamini and Hochberg 1995) implemented by the 'statmodels' Python package to adjust the p-values used to identify the statistical significance of correlations. A binary classification system was applied to eligible datasets, whereby datasets were classed as either water-limited or energy-limited if at least 66% of the significant correlations were positive or negative respectively. A sensitivity analysis showed that changing the thresholds for categorisation had minimal influence on the overall results, and thus thresholds were selected to balance stringency and dataset retention (supplementary figure 2, supplementary table 3).

In addition to P-ET relationships, correlations were computed between monthly anomalies of other variables to fully assess model representation of physical processes in the Amazon hydrological cycle, including P-CLD, P-SM, RDN-CLD, RDN-P, RDN-ET and SM-ET relationships. We tested how P-ET, RDN-ET and SM-ET relationships responded to spatial variation in P, considering water-limited and energy-limited models separately. Correlation coefficients for all Amazon grid cells were binned by mean annual P, using a bin width of 50 mm. Bins with fewer than five data points were excluded from the analysis.

We assessed whether differences in model representation of Amazon ET controls influenced Amazon P projections. For this, we used simulations from the representative concentration pathway (RCP) 8.5 experiment, a future-change scenario with high radiative forcing at the end of the century (Riahi et al 2011). Change anomalies were calculated at the annual time scale (using data from all months, or three-monthly periods) for 2008–2099, taking 1980–1999 as the historical reference period. Interannual data were smoothed with an 11 year moving average to better visualise inter-decadal trends (Boisier et al 2015). Reported end-of-century changes represent the mean P anomaly across the 20 year period from 2080 to 2099 (ΔP). We used a Monte Carlo-type approach to determine whether the standard deviation (σ) in basin-mean ΔP across the 13 energy-limited CMIP5 models was different to what might be expected by chance (supplementary methods 1.4).

To test the hypothesis that the smaller future range in P projections in energy-limited models was influenced by climate buffering due to the negative relationship between P and ET, we examined ΔP together with changes in ET and RDN (ΔET and ΔRDN) at the grid-cell scale by the end of the century (2080–2099), using 1980–1999 as the historical reference period. We calculated linear regression relationships between ΔP and ΔET and between ΔRDN and δET, where δET represents the difference between the actual simulated ΔET in the grid cell, and the ΔET predicted from ΔP using the linear ΔP-ΔET relationship derived from all models, accounting for uncertainty along both axes (York 1966). Relationships were calculated for all, energy-limited and water-limited models, using data from all Amazon grid cells.

Amazon P-ET correlations based on ET estimates from satellites, flux-tower measurements and reanalysis were predominantly negative (figures 1(b)–(d), supplementary figure 3), providing strong evidence that Amazon ET is primarily energy-limited, in agreement with earlier studies (Fisher et al 2009, Sun et al 2019). All but one of the ET products analysed showed good agreement in the direction of correlations, particularly over the northern Amazon, though there were some spatial differences elsewhere (supplementary figure 4). Furthermore, the single satellite ET product that showed opposing results has previously been shown to perform poorly in the Amazon (Miralles et al 2011, Baker et al 2021b).

Strikingly, only 13 out of 38 CMIP5 models captured an energy control on Amazon ET (hereafter energy-limited models), while 20 models instead showed Amazon ET was limited by water availability (hereafter water-limited models, supplementary figure 3). The spatial pattern of P-ET relationships in energy-limited models matched well with observations, particularly in the northwest Amazon where there was good agreement among models (figure 1(e), supplementary figure 4). In contrast, water-limited models showed positive P-ET correlations over the whole basin (figure 1(f)). Given that nearly half of CMIP5 models simulated the wrong controls on Amazon moisture fluxes, the multi-model ensemble provides a poor representation of the observed state (figure 1(g)). Trying to understand future changes in Amazon hydrology through an assessment of the ensemble mean is therefore unlikely to yield reliable results. The division of CMIP5 models into two populations with opposing controls on Amazon ET was supported by a Budyko drought-index analysis, whereby the ratio of potential ET (PET) to P indicates an energy-limited (PET/P < 1) or water-limited (PET/P > 1) evaporative regime (supplementary methods 1.2, supplementary figure 5). Together, these results highlight a potential source of divergence in simulations of the Amazon hydrological cycle among CMIP5 models. Finally, we repeated our analysis using newly-available historical simulations from 26 CMIP6 models and found consistent results (supplementary figure 6), indicating that our findings from CMIP5 are generalizable to the latest generation of climate models.

Land–atmosphere interactions in CMIP5 models can be modulated by background P (Berg and Sheffield 2018), so we tested whether differences in P could explain differences in ET controls between the two model populations. Models that captured an energy limitation on Amazon ET tended to be wetter over the whole Amazon, and simulated mean annual P closer to observations (supplementary figure 7). The five wettest models were all energy-limited, suggesting that simulating a sufficiently high background Amazon P may be a first step towards capturing the right controls on ET. However, there were exceptions to this pattern, with some drier models still simulating a radiation control on Amazon ET, and wetter models where ET was found to be water-limited. When we examined how P-ET relationships responded to spatial variation in P, we found that energy and water-limited models simulated opposite controls on ET over the same range in P (figure 2). Models in the energy-limited population showed a relatively sharp transition from positive to negative P-ET correlation coefficients when P reached around 1500 mm yr⁻¹, followed by a more gradual decline in correlation as annual P continued to rise (figure 2). This behaviour, which is supported by the majority of observations (figure 2), is consistent with hydrological theory (Budyko 1974), and our current understanding of the controls on Amazon photosynthesis (Guan et al 2015). In contrast, water-limited models showed positive P-ET correlations until P reached nearly 3000 mm yr⁻¹, suggesting they fail to accurately represent the physical processes that modulate ET over the Amazon.

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Models also exhibited differences in behaviour in response to temporal variation in P. Although all models simulated Amazon P seasonality relatively well (supplementary figure 8), energy-limited models reproduced a strong seasonal cycle in P-ET correlations, as shown in observations, while water-limited models showed little variation in P-ET correlations throughout the year (supplementary figure 9). Energy-limited models showed a clear pattern of behaviour with varying water availability, simulating negative P-ET correlations in months where mean Amazon P exceeded 200 mm month⁻¹ (November–April) and positive P-ET correlations in the driest part of the year (July–September). Meanwhile, water-limited models simulated positive P-ET correlations in all months, including months where simulated Amazon P was greater than 200 mm month⁻¹ (December–March). These results, together with the results presented in figure 2, demonstrate that although differences in background P may explain some of the differences between energy and water-limited models, there also appears to be a more fundamental difference in model behaviour between the two groups in their ability to respond to changing background conditions. Since controls on ET may evolve with changing climate, capturing a switch in ET controls with changing P has implications for future projections.

To better understand the physical processes causing differences in behaviour among climate models, we evaluated relationships along the full hydrological pathway (figure 3). Both groups of models generally captured relationships between variables in the two branches of figure 1(a), with the exception of correlations between RDN and ET, and between SM and ET. Water-limited models tended to underestimate and overestimate RDN-ET and SM-ET relationship strengths respectively, relative to those seen in observations and energy-limited models (figure 3, supplementary figures 10 and 11). We found SM-ET correlations in the two model populations showed divergent responses to increasing annual P that were comparable to the responses of P-ET relationships, while RDN-ET correlations showed more similar behaviour (figure 2, supplementary figure 12). This result suggests that models differ in their ability to represent realistic P-ET correlations over the Amazon due to differences in processes related to the soil-plant-atmosphere moisture-transport pathway, highlighting an area for future model development.

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By identifying models that were able to correctly reproduce key land–atmosphere interactions in the historical period, we could constrain future projections of Amazon P. Models that correctly captured an energy limitation on Amazon ET showed a highly constrained future P response when compared to water-limited models (figure 4(a)). The standard deviation in end-of-century ΔP values was halved in energy-limited models (σ = 4.35 vs 9.25%, representing a 53% difference), and smaller than expected by chance (estimated through repeated random selection of 13 models from the pool of 38 models, supplementary figure 13). Removal of the water-limited model with the most negative ΔP response (CanEMS2), caused only a slight reduction to the difference in spread between the two model groups (σ = 4.35 vs 7.01%, representing a 38% difference), suggesting our results are relatively robust. The water-limited models showed lower coherence in P trends, tending to predict more extreme changes, both positive and negative, in Amazon P than energy-limited models (figure 4(a)). This difference in behaviour can be understood by considering the sign of relationships between P and ET in the two model groups (figure 1(a)). Water-limited models showed a positive correlation between monthly anomalies of P and ET, so any increase (or decrease) in P is likely to be further enhanced, making simulation of extreme changes more likely. On the other hand, energy-limited models had a negative correlation between P and ET, such that Amazon climate will tend to show a buffered response to change. We tested whether this mechanism operated on climate-change timescales through examining climate anomalies at the end of century (ΔP, ΔET and ΔRDN). ΔET was strongly positively related to ΔP across all models (figures 4(b)–(d)), showing the net response of the coupled land-atmosphere system across energy-limited and water-limited models is to simulate increasing ET with increasing P under climate change (and vice versa). However, the greater correlation (r = 0.74 vs 0.61) and steeper slope (0.53 vs 0.47) in models where ET is water-limited is indicative of a greater role of ΔP in determining ΔET in the climate change response of these models. More significantly, the difference between the actual simulated ΔET change per Amazon grid cell and the change predicted from grid-cell level ΔP using the all-model regression relationship (ΔET_actual − ΔET_predicted = δET) was shown to be almost twice as strongly influenced by ΔRDN in models that captured an energy limitation on Amazon ET over the historical period, compared with those that simulated a water limitation (slope = 0.051 vs 0.029 mm d⁻¹/W m⁻²), with much greater correlation between ΔRDN and δET in energy-limited models (r = 0.46 vs 0.19; figures 4(f) and (g)). Thus, ΔRDN modulates the climate-change response in energy-limited models such that for a given value of ΔP, energy-limited (water-limited) models will show a smaller (larger) ΔET response, thus dampening (amplifying) the P anomaly.

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We examined whether variation in model set-up might contribute to the observed differences in P projections between the two model populations (supplementary table 1). Dynamic vegetation (simulation of changes in vegetation types in response to climate) was more common among water-limited models than energy-limited models (55 vs 23%, p = 0.070, chi-squared statistic), consistent with a recent study showing dynamic global vegetation models generally struggle to capture radiation controls on productivity in tropical regions (O'Sullivan et al 2020). However, inclusion of dynamic vegetation had no clear influence on the direction or magnitude of ΔP (supplementary figure 14), and therefore did not contribute to the observed differences between water-limited and energy-limited CMIP5 models. We also compared model inclusion of the CO₂ physiological effect, where plants reduce their stomatal conductance in response to increased atmospheric CO₂, but the frequency of this feature among the two model groups was similar (76 vs 65% of water-limited models, p = 0.21). Likewise, there was no difference in the proportion of energy-limited and water-limited models that included future land-use-change forcing (76 vs 70%, p = 0.66). Only four CMIP5 models simulated a nitrogen limitation on photosynthesis and these were all energy-limited models (supplementary table 2). However, given the small number of models including this process (albeit a third of all energy-limited models), we hesitate to draw definite conclusions about the role of nitrogen limitation in influencing ET controls.

Spatial patterns in ΔP were more distinctive in energy-limited models, which simulated annual drying of up to 26% (ΔP_absolute = –1.3 mm d⁻¹) over the eastern Amazon, and wetting in the west (<23%, 1.8 mm d⁻¹, figure 5(a)), with at least 75% agreement among models in the direction of change (supplementary figure 15). ΔET maps showed a similar dipole response (supplementary figure 16). Meanwhile, P changes in water-limited models were comparably weaker and more uncertain (drying <13%, wetting <16%, figure 5(b), supplementary figure 15).

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Analysis of seasonal ΔP changes provided further evidence for a difference in climate-buffering capability between model populations. Water-limited models, which showed higher and less realistic seasonal P variability over the historical period, simulated stronger increases in seasonality over the next century than energy-limited models (figure 5(c)). However, though smaller in magnitude, the increase in P seasonality was actually more robust in energy-limited models, due to the smaller spread in projections (figure 5(d)). Basin-mean P reductions in energy-limited models were concentrated in the dry season (July–September) and the start of the wet season (October–December), with marginal P increases at other times of the year (supplementary figure 17). The dry season response was particularly striking, with energy-limited models unanimously showing a drying by the end of the century (basin-mean ΔP ± σ = −14.3 ± 6.5 vs −14.9 ± 26.8% in water-limited models; supplementary figure 17), and P reductions of up to 50% over some areas of the eastern Amazon (supplementary figure 18). Overall, these results show that discounting models with unrealistic land–atmosphere interactions revealed more robust future P changes over the Amazon than projected by the full model ensemble, thus substantially reducing uncertainty in future Amazon P.

Energy-limited models, in which controls on ET showed realistic sensitivity to spatial and temporal variation in P (figure 2, supplementary figure 9), showed a shift in land–atmosphere interactions in response to future changes in climate (figure 6). Amazon ET becomes increasingly water-limited by the end of the century, which will reduce the buffering capacity of the climate system. In contrast, water-limited models showed no change in P-ET correlations, consistent with their limited responsiveness to changing background conditions over the historical period (figure 2, supplementary figure 9). The dynamic behaviour displayed by energy-limited models in response to changing water availability illustrates why process-based model evaluation is fundamental to assessments of model performance and highlights the fact that, despite the stabilising mechanism of an inverse P-ET relationship, the Amazon hydrological cycle remains vulnerable to the impacts of climate change.

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