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Article Type:
Research Article

The Amazon Water Cycle: Perspectives from Water Budget Closure and Ocean Salinity

J. E. Jack Reeves Eyre Department of Hydrology and Atmospheric Sciences, The University of Arizona, Tucson, Arizona

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Xubin Zeng Department of Hydrology and Atmospheric Sciences, The University of Arizona, Tucson, Arizona

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Online Publication:
25 Jan 2021
Print Publication:
01 Feb 2021
DOI:
https://doi.org/10.1175/JCLI-D-20-0309.1
Page(s):
1439–1451
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Abstract

Global and regional water cycle includes precipitation, water vapor divergence, and change of column water vapor in the atmosphere, and land surface evapotranspiration, terrestrial water storage change, and river discharge, which is linked to ocean salinity near the river mouth. The water cycle is a crucial component of the Earth system, and numerous studies have addressed its individual components (e.g., precipitation). Here we assess, for the first time, if remote sensing and reanalysis datasets can accurately and self-consistently portray the Amazon water cycle. This is further assisted with satellite ocean salinity measurements near the mouth of the Amazon River. The widely used practice of taking the mean of an ensemble of datasets to represent water cycle components (e.g., precipitation) can produce large biases in water cycle closure. Closure is achieved with only a small subset of data combinations (e.g., ERA5 precipitation and evapotranspiration plus GRACE satellite terrestrial water storage), which rules out the lower precipitation and higher evapotranspiration estimates, providing valuable constraints on assessments of precipitation, evapotranspiration, and their ratio. The common approach of using the Óbidos stream gauge (located hundreds of kilometers from the river mouth) multiplied by a constant (1.25) to represent the entire Amazon discharge is found to misrepresent the seasonal cycle, and this can affect the apparent influence of Amazon discharge on tropical Atlantic salinity.

Current affiliation: Cooperative Institute for Climate, Ocean and Ecosystem Studies, University of Washington, Seattle, Washington.

Supplemental information related to this paper is available at the Journals Online website: https://doi.org/10.1175/JCLI-D-20-0309.s1.

© 2021 American Meteorological Society. For information regarding reuse of this content and general copyright information, consult the AMS Copyright Policy (www.ametsoc.org/PUBSReuseLicenses).

Corresponding author: Jack Reeves Eyre, jack.reeveseyre@gmail.com

Abstract

Global and regional water cycle includes precipitation, water vapor divergence, and change of column water vapor in the atmosphere, and land surface evapotranspiration, terrestrial water storage change, and river discharge, which is linked to ocean salinity near the river mouth. The water cycle is a crucial component of the Earth system, and numerous studies have addressed its individual components (e.g., precipitation). Here we assess, for the first time, if remote sensing and reanalysis datasets can accurately and self-consistently portray the Amazon water cycle. This is further assisted with satellite ocean salinity measurements near the mouth of the Amazon River. The widely used practice of taking the mean of an ensemble of datasets to represent water cycle components (e.g., precipitation) can produce large biases in water cycle closure. Closure is achieved with only a small subset of data combinations (e.g., ERA5 precipitation and evapotranspiration plus GRACE satellite terrestrial water storage), which rules out the lower precipitation and higher evapotranspiration estimates, providing valuable constraints on assessments of precipitation, evapotranspiration, and their ratio. The common approach of using the Óbidos stream gauge (located hundreds of kilometers from the river mouth) multiplied by a constant (1.25) to represent the entire Amazon discharge is found to misrepresent the seasonal cycle, and this can affect the apparent influence of Amazon discharge on tropical Atlantic salinity.

Current affiliation: Cooperative Institute for Climate, Ocean and Ecosystem Studies, University of Washington, Seattle, Washington.

Supplemental information related to this paper is available at the Journals Online website: https://doi.org/10.1175/JCLI-D-20-0309.s1.

© 2021 American Meteorological Society. For information regarding reuse of this content and general copyright information, consult the AMS Copyright Policy (www.ametsoc.org/PUBSReuseLicenses).

Corresponding author: Jack Reeves Eyre, jack.reeveseyre@gmail.com
Keywords: Amazon region; Freshwater; Precipitation; Runoff; Water budget/balance

1. Introduction

Earth’s water cycle is of primary interest for both the day-to-day needs of human life and the evolution of human civilization. Mean patterns of precipitation control water availability and crop viability. Water cycle variability and extremes create deadly floods and devastating droughts. Long-term changes, whether natural (e.g., desertification of the Sahara; Tierney et al. 2017) or anthropogenic (e.g., drying up of the Aral Sea), can shape entire industries (Micklin 2016) and even societies (Kuper and Kröpelin 2006). Climate change and deforestation have raised fears that the water cycle (and, with it, the carbon cycle) of the Amazon basin may undergo similar widespread change in the coming decades (Nobre et al. 2016), with regional and potentially global consequences. To understand if, when, and how such changes could occur requires accurate knowledge of the current state and past variability of water cycle processes. In this paper we investigate the ability of widely used global climate datasets to provide not only an accurate representation of individual processes, but also a consistent picture of multiple aspects of the water cycle.

The primary processes of the global water cycle are precipitation and evaporation, terrestrial storage and flow of water (on and below the land surface), and atmospheric transport of water vapor. Spatial patterns of evaporation and precipitation show large latitudinal gradients and land–sea contrast. On average, precipitation exceeds evaporation over land, while evaporation exceeds precipitation over the ocean (e.g., Schlosser and Houser 2007). The atmosphere transports water from ocean to land, while rivers transport water from land to oceans.

Measurement of water cycle processes presents significant challenges. Point measurements of precipitation and sometimes river discharge can be made by relatively cheap and accurate automated systems. Evapotranspiration and terrestrial water storage, on the other hand, require complicated, expensive, and labor-intensive techniques. For all quantities except river discharge, which naturally integrates over a wide area, estimation of areal averages from sparse point measurements is a large part of the problem (e.g., Wigley et al. 1984). Satellite remote sensing and modeling naturally help alleviate this difficulty. Precipitation can be estimated from rain gauges and satellite remote sensing, and many global estimates of evapotranspiration have also been developed in recent decades (Mueller et al. 2011), based on combinations of remotely sensed data and models. Meanwhile, for terrestrial water storage, GRACE satellites (Tapley et al. 2004) have revolutionized our understanding of large-scale hydrology (among other branches of Earth science; Tapley et al. 2019). Thus, while there are many data sources which are applicable to water cycle studies, knowing which provide accurate and reliable data represents a further challenge. Addressing that challenge is the central theme of this study.

The Amazon River is the largest on Earth, by discharge and drainage area. The large basin area means that the climate monitoring network is rather sparse (e.g., gauge-based analyses typically rely on around 750 rain gauges across the basin; Guimberteau et al. 2012) and therefore understanding the water cycle of the Amazon relies on the kind of remote sensing and model data sources discussed above. In this respect, the Amazon is an important case as it provides more specific information on available data sources than global and continental-scale studies but is large enough for robust remote sensing (i.e., without large biases caused by masking a relatively coarse data grid to irregular basin boundaries). The Amazon does (perhaps again due to its size and importance) also have a number of long-running stream gauging stations. The farthest downstream is at Óbidos, around 700 km upstream from the river mouth. The drainage area of this station is approximately 80% of the total Amazon basin area (see Fig. S1 in the online supplemental material). Óbidos discharge is commonly used to represent the discharge of the entire Amazon, either in raw form or after multiplication by a scaling factor [e.g., the CORE II ocean model forcing dataset (Large and Yeager 2004, 2009) makes use of the scaled discharge estimate of Dai and Trenberth (2002)]. While this approach may be appropriate for many applications, it may not accurately characterize seasonal variation of Amazon discharge, due to possible differences across the basin in the seasonal variations of water cycle processes. We address this issue as part of our investigations here.

When it comes to assessing and choosing global datasets for water (and energy) cycle studies, the importance of self-consistent combinations of datasets has recently been highlighted by GEWEX (Kummerow 2019). Comparison with in situ measurements provides valuable insights, but is not without uncertainties (Gebremichael and Krajewski 2005) especially in regions where in situ data are sparse—the very places in most need of alternative data sources. A further disadvantage to validation using in situ data is that it tends to address only one variable at a time, and therefore there is no guarantee of a consistent view of the entire water cycle, including with respect to water budget closure. Closure has been used as a test of data realism and consistency in global studies (e.g., Trenberth et al. 2011; Trenberth and Fasullo 2013; Rodell et al. 2015). However, when it comes to regional studies, it is more common either to assume or to enforce closure: Syed et al. (2005) assume closure to estimate discharge of the Amazon based on the other terms in the water budget, while Rodell et al. (2011) do the same to estimate evapotranspiration. Pan et al. (2012) enforce closure for the water budgets of a number of major global rivers, dividing the residual among different water cycle terms based on their estimated uncertainties. Our approach in this work is to take what has been the global approach—to test closure—and apply it to the Amazon basin. In this way, we use closure as a test of both the accuracy of individual datasets and their ability to form part of a consistent picture of the entire water cycle.

A shared feature of many water cycle studies is their handling of different datasets for the same variables. Both regional (e.g., Sahoo et al. 2011) and global (e.g., Mueller et al. 2013) studies have often used ensemble means of available datasets. This is a pragmatic approach to dealing with uncertainty but has several disadvantages: in its simplest flavor, it gives undue influence to outliers; more complicated (e.g., weighted, variational) versions rely on assumptions about relative uncertainties of different datasets; the result is sensitive to the rather arbitrary choice of which datasets to include, and how to deal with datasets that have strong similarities (e.g., different versions of the same model). Therefore a further aim of this study is to test how suitable the ensemble mean approach is for water cycle studies, again using closure to test how well the ensemble mean performs compared to individual datasets.

Beyond closure, further insights into consistency between datasets can be gained from considering the effects of Amazon discharge on salinity of the adjacent ocean [similar in spirit, though not in methods, to Gouveia et al. (2019) and Pellet et al. (2019)]. The Amazon freshwater plume extends for several thousand kilometers through the tropical Atlantic, going northward, toward, and even into the Caribbean Sea, and eastward, toward Africa, in the North Equatorial Countercurrent. As it does so, it affects salinity and thereby water stratification (Reeves Eyre et al. 2019) and ocean surface heat fluxes (Rudzin et al. 2019) over a wide area. However, before it spreads out and is diluted over a wide region of the Atlantic, it is confined to a relatively narrow band in the North Brazil Current. We investigate whether the salinity in this region can be used as a consistency check for different water cycle dataset combinations. We do this by calculating water balance-based estimates of discharge and using their correlations with salinity to differentiate between data combinations. This builds on the work of Hellweger and Gordon (2002), who showed that the seasonal cycle of salinity at Barbados can largely be explained by Amazon discharge, and Salisbury et al. (2011), who suggested that salinity is strongly affected by discharge over quite a long stretch of the plume. At this point, it should be noted that other studies have found that ocean currents and local precipitation dominate the salinity variability in the tropical Atlantic (e.g., Fournier et al. 2017; Coles et al. 2013; Masson and Delecluse 2001). While some of the disagreement between results in the literature is likely due to differing methods and study regions, we ask if perceived influence of discharge is dependent on discharge estimation methods. As noted by Hellweger and Gordon (2002) and Salisbury et al. (2011), the use of Óbidos discharge to represent the entire Amazon basin may misrepresent both the amount and seasonal variation. Thus water balance estimates of Amazon discharge provide means to use salinity to tell us about discharge and to use discharge to tell us about salinity.

The main science questions we aim to answer in this study are the following: 1) Do global remote sensing and reanalysis products agree on water budget terms, and can they close the water budget over the Amazon? 2) Do ensemble mean products close the Amazon water budget better than the individual datasets that go into them? 3) Can ocean salinity near the mouth of the Amazon be used as a further test of terrestrial water cycle datasets? 4) Does consideration of closure and/or ocean salinity criteria reduce the range of plausible estimates for any water cycle components? In the next section, we describe the data used in this study. In section 3, we ask which combinations of data close the water budget. Next, in section 4 we test whether ocean salinity provides further constraints on the Amazon water cycle. Finally, in section 5 we present further discussion and summarize our findings.

2. Methods and data

a. Study area

To delineate the Amazon basin, we use a shapefile (as commonly used in geographic information system software) from HYBAM (the National Observation Service for Hydrology of the Amazon Basin; HYBAM 2019). This gives a basin area of 6.07 × 106 km2. HYBAM maintains a number of stream gauges across the Amazon basin. For practical reasons (including tidal effects on the river further downstream) the farthest downstream gauge is around 700 km from the mouth of the river, at Óbidos. The catchment area of this stream gauge (4.76 × 106 km2) is around 78% of the area of the entire basin, and the ungauged 22% contributes a significant amount of discharge. Dai and Trenberth (2002) and Dai et al. (2009) estimate the discharge of the entire basin as RAmazon = 1.25 × RÓbidos. These studies used land model simulations to calculate the 1.25 factor from the ratio of R at the gauge (i.e., Óbidos) and river mouth locations. We use this as a “prior” estimate for the Amazon discharge, but the investigation of this issue is one of the subjects of this work. The Amazon basin and Óbidos catchment are shown in Figs. S1 and S2.

b. Methods

1) Water budget

The terrestrial water budget equation is
P−E−R=dSterrdt,
where P is precipitation, E is evapotranspiration, R is river discharge (or streamflow), and dSterr/dt is rate of change of terrestrial water storage, all with dimensions of volume per time (or length per time if normalized by area). The atmospheric water budget is
E−P−∇⋅(qv)=dSatmdt,
where P and E are as in Eq. (1), ∇ (qv) is divergence of atmospheric water vapor, and dSatm/dt is the rate of change of atmosphere total column water vapor. Note that P − E can be eliminated from Eqs. (1) and (2) to give an alternative “atmospheric convergence” form of the terrestrial water budget:
−∇⋅(qv)−dSatmdt−R=dSterrdt.
We use monthly means for all flux terms. GRACE provides monthly mean Sterr (relative to an arbitrary baseline), so we calculate its rate of change (and, to be consistent, that of Satm) using a fourth-order centered difference:
dXdt|i=112Xi−2−23Xi−1+23Xi+1−112Xi+2,
where Xi stands for Sterr or Satm for month i. This method [Eq. (4)] is similar to those of Eicker et al. (2016) and Pellet et al. (2019) and has an advantage over other approaches (e.g., Rodell et al. 2004a; Syed et al. 2005) in that it allows use of Eq. (1) with monthly, as opposed to just daily and subdaily, P and E datasets. For seasonal and annual rates of change of Sterr and Satm, we use a simpler second-order forward difference, although our main results and conclusions would not be affected if we instead took the seasonal or annual average of the monthly values from Eq. (4).
When using Eqs. (1) and (3) with real-world data, it is virtually certain that the budgets will not close. Throughout this work we refer to the closure residuals, defined as
ε=P−E−R−dSterrdt
(and similarly for the convergence method). We look at the mean values ε¯ and mean absolute values |ε|¯ for various combinations of P, E, and so on. We also make use of water-budget based estimates of discharge:
R^=P−E−dSterrdt
(and similarly for the convergence method), focusing particularly on the comparisons between R^ and R and between R^ and ocean salinity. We use Eqs. (1)–(6) with various combinations of data, described in the following subsections. Datasets are spatially averaged to the appropriate region (Amazon basin or Óbidos catchment) before substitution into the equations.

2) Uncertainty analysis

The definition of R^ also forms the basis for our uncertainty analysis: we compare samples of R and R^, using Welch’s (unequal variance) two-sample t test. The null hypothesis is that R and R^ come from the same population. Rejection of the null hypothesis tells us that R^ differs from R by an amount that is, in some sense, large compared to the interannual variability of R. We perform the test separately on samples from each month and season, and count the number of months or seasons for which the null hypothesis is rejected. Welch’s t test assumes that both samples are normally distributed; this is tested using the Shapiro–Wilk test. This method is chosen instead of estimating and combining separate uncertainties for all water budget terms (as in, e.g., Syed et al. 2005) because it avoids the rather arbitrary estimates of uncertainty for most water budget terms.

c. Data

1) Precipitation

We use monthly average precipitation from three satellite-based products and two atmospheric reanalyses, described here. Spatial distributions of annual mean precipitation from the five datasets are shown in Fig. S1 in the supplemental material. GPCP (the Global Precipitation Climatology Project, version 2.3; Adler et al. 2003, 2018) is a satellite-gauge blended product. It is produced on a 2.5° × 2.5° global grid, and is available for the period 1979 to the present. CMAP (CPC Merged Analysis of Precipitation; Xie and Arkin 1997; NOAA CPC 1997), like GPCP, is a satellite-gauge blended product on a 2.5° × 2.5° global grid. It covers the period 1979–2019. CHIRPS (Climate Hazards Group Infrared Precipitation with Stations; Funk et al. 2014a,b) is a high-resolution (0.05°) satellite–gauge merged product available for latitudes 50°S–50°N (and all longitudes), covering the period 1981–2019.

The two reanalyses used are ERA5 (Copernicus Climate Change Service 2017) and MERRA-2 (Gelaro et al. 2017; NASA GMAO 2015a,b,c). ERA5 covers the period 1979–present and is available on 0.25° × 0.25° global grid. MERRA-2 is available for the period 1980 to the present on a global 0.5° latitude × 0.625° longitude grid. MERRA-2 uses a precipitation bias correction (Reichle et al. 2016) that adjusts the precipitation “seen” by the land surface, toward the CPC Unified Gauge-Based Analysis of Global Daily Precipitation (CPCU) product. Reichle et al. (2016) showed that globally the bias correction results in improvements, but that over the Amazon the correction actually results in a deterioration after 2005, because CPCU differs significantly from the more accurate reference observational product (GPCP v2.2) after this time. MERRA-2 data products include both the corrected and uncorrected precipitation. We use the corrected product, despite the deterioration noted, because the uncorrected version gives very similar results to the atmospheric moisture convergence method (see below): using the corrected precipitation therefore provides greater diversity of results.

2) Evapotranspiration

We use monthly average evapotranspiration (not latent heat flux) from two atmosphere–land reanalyses (ERA5 and MERRA-2; described above), two land reanalyses, and one “standalone” evapotranspiration model. Spatial distributions of annual mean evapotranspiration from the five datasets are shown in Fig. S2 in the supplemental material. The evapotranspiration model is GLEAM (Global Land Evaporation Amsterdam Model; Martens et al. 2017a,b; Miralles et al. 2011), which comes in several different versions differing mainly in their forcing datasets. We use v3.3b (forced mainly by satellite data), which is produced on a 0.25° × 0.25° global grid and covers the period 2003 to 2018. Two datasets from the Global Land Data Assimilation System (GLDAS; Rodell et al. 2004b) are used: one uses the Community Land Model (CLM version 2.0) with output on a 1° × 1° global grid for the period 1979 to present (Rodell and Beaudoing 2007); the other uses the Noah land surface model (version 3.6) and is available from 2000 to 2019 on a 1° × 1° global grid (Beaudoing and Rodell 2020).

3) Atmospheric moisture and convergence

We apply Eq. (3) with data from the two reanalyses (ERA5 and MERRA-2; described above). Convergence of atmospheric moisture vapor [−∇(qv)] is available directly from the reanalyses, as monthly averages of time step moisture divergence. Basin-averaged −∇(qv) is almost equal to P − E for ERA5 but not for MERRA-2, due to the bias correction discussed above. The change in total column water [dSatm/dt; calculated from Satm using Eq. (4)] is of smaller magnitude, but is included nonetheless for completeness.

4) Terrestrial water storage

We use monthly Sterr from three GRACE retrievals: JPL (the Jet Propulsion Laboratory; Watkins et al. 2015; Wiese et al. 2018), CSR (Center for Space Research; Save et al. 2016; Save 2019), and GFZ (GeoForschungsZentrum, the German Research Centre for Geosciences; Dahle et al. 2019; Dahle and Murböck 2019). These are provided on regular global grids at, respectively, 0.5°, 0.25°, and 1.0° resolution and all cover the same period (2002–17). The differences between the three are small in our application, so most of the following results use only the JPL retrieval.

5) River discharge

Monthly average discharge measured at Óbidos, the farthest downstream gauging station on the Amazon, was downloaded from HYBAM (HYBAM 2019). This dataset covers the period 1968–2018, and is based on a stage–discharge relationship with seasonally varying parameters, due to changes in channel properties (Mansanarez et al. 2016). Discharge is estimated for the entire Amazon using the method of Dai and Trenberth (2002) and Dai et al. (2009).

6) Data combinations and ensemble means

Water budgets are constructed with different data combinations. Five precipitation (GPCP, CMAP, CHIRPS, ERA5, MERRA-2) with five evapotranspiration (GLEAM, CLM, Noah, ERA5, MERRA-2) sources gives 25 combinations, which we refer to with the form PEG_precip_evap_GRACE (e.g., PEG_GPCP_GLEAM_JPL; “PEG” stands for precipitation-evapotranspiration-GRACE). This could be extended to 75 combinations with the three GRACE retrievals, but we do not as the differences between GRACE retrievals are small. Even without this, it is clear that the proliferation of water cycle datasets has increased the number of possible combinations compared to Marengo (2005). Two combinations are constructed from the two reanalysis convergence quantities: CHG_ERA5_ERA5_JPL and CHG_MERRA2_MERRA2_JPL (“CHG” stands for convergence-humidity-GRACE). Two further combinations are constructed from ensemble means. PEG_Ens uses, for precipitation, the mean of GPCP, CMAP, CHIRPS, ERA5, and MERRA-2 precipitation; for evapotranspiration, the mean of GLEAM, CLM, Noah, ERA5, and MERRA-2; and for terrestrial water storage, the mean of the JPL, CSR, and GFZ retrievals. The second ensemble combination, denoted CHG_Ens, uses the atmospheric convergence method with the mean of ERA5 and MERRA-2 for both moisture convergence and total column water, and the mean of the JPL, CSR, and GFZ retrievals for terrestrial water storage.

7) Ocean salinity

We use sea surface salinity from the SMOS satellite (level 3, version 3; Boutin et al. 2018a; Kerr et al. 2016; Boutin et al. 2018b) as it has a longer record (2010–17) than alternatives such as the SMAP (Soil Moisture Active Passive; 2015–19) and Aquarius (2011–15) satellites (Meissner et al. 2018; Fore et al. 2016; Lee et al. 2012). A detailed global comparison of these three data sources is given by Bao et al. (2019). When comparing these three salinity products in the tropical Atlantic (Fig. S3), we find relatively large differences around the mouth of the Amazon. However, they have high correlations in the Amazon plume region, which we take to demonstrate good agreement in salinity variability. SMOS data are provided as 4-day averages on an (approximately) 25 km × 25 km grid: we aggregate to monthly and interpolate to a regular 1° grid.

3. Water budget closure

The datasets analyzed here for each component of the water cycle give a relatively clear qualitative picture of the seasonal cycle in the Amazon (Fig. 1). Precipitation has a strong seasonal cycle, as do terrestrial water storage change (which varies approximately in phase with precipitation) and discharge (which, at Óbidos, lags precipitation by 3–4 months). Evapotranspiration has a relatively weak seasonal cycle, in agreement with Getirana et al. (2014). It should be noted that this weak basinwide seasonal cycle hides larger regional variations (Paca et al. 2019). Spread among datasets (shown by shading in Fig. 1) is considerable for precipitation and evapotranspiration, and the spreads appear to have their own seasonal cycle: precipitation spread is largest from November to April, while evapotranspiration spread is largest from June to September. Differences among GRACE terrestrial water storage change retrievals are much smaller than the spread in precipitation and evapotranspiration datasets. This may well reflect the fact that all three retrievals use similar methods on the same underlying data, so their differences do not fully sample the uncertainties and biases of the GRACE data and retrieval methods. Whatever the cause of their similarity, this result justifies the use of a single retrieval in order to simplify the interpretation of further results. Most of the analysis presented below therefore only uses the JPL retrieval.

Fig. 1.
Fig. 1.

Mean annual cycles of Amazon basin water cycle components: precipitation (cyan), evapotranspiration (pink), change in terrestrial water storage (purple), discharge (black), and the closure residual (yellow). For precipitation, evapotranspiration, and terrestrial water storage change, the thick line shows the ensemble mean and shading represents the ensemble spread (maximum to minimum). The discharge for the entire Amazon basin is estimated using Óbidos discharge multiplied by 1.25 (following Dai et al. 2009). Water budget closure residuals are shown for two combinations: one (solid line; referred to as PEG_Ens) uses the ensemble means of precipitation, evapotranspiration. and terrestrial water storage change, while the other (dashed line; referred to as PEG_ERA5_ERA5_JPL) uses ERA5 precipitation and evapotranspiration and JPL terrestrial water storage change.

Citation: Journal of Climate 34, 4; 10.1175/JCLI-D-20-0309.1

Residuals from water budget closure are shown in Fig. 1 for two data combinations: PEG_Ens and PEG_ERA5_ERA5_JPL. Strikingly, the residuals for PEG_Ens are significantly larger than those for PEG_ERA5_ERA5_JPL, with the largest differences from October to May. The residuals for PEG_Ens reach ~50% of the Amazon discharge—a value that, qualitatively at least, would seem to represent a major departure from water budget closure.

The residual results are summarized for all data combinations in Fig. 2. A number of combinations have mean residuals with magnitude as large as, or larger than, those of PEG_Ens, while few have mean residuals as small as PEG_ERA5_ERA5_JPL. The spread of residuals is similar at monthly, seasonal, and annual time scales, showing that, as for PEG_Ens in Fig. 1, residuals are of a consistent sign across different months of the year. For a few combinations—those, like PEG_ERA5_ERA5_JPL in Fig. 1, with relatively small residuals that change from positive to negative at different times of year—the mean absolute residual (not shown) is smaller at annual time scales than monthly and seasonal.

Fig. 2.
Fig. 2.

Mean residuals of water budgets for Óbidos catchment area and entire Amazon basin at (left) monthly, (center) seasonal, and (right) annual time scales, expressed as a fraction of annual mean discharge. Residuals for Amazon catchment use Óbidos discharge multiplied by 1.25. Each point represents one combination of water budget terms (e.g., PEG_ERA5_ERA5_JPL). For monthly and seasonal panels, points are colored according to the count of months or seasons (respectively) that result in a significant difference between discharge R and R^, based on Welch’s (unequal variance) t test with a significance level α = 0.05. For the annual plot, points are colored according to whether the distribution of annual means differ according to the same test (for a null hypothesis that the distributions are the same, 0 means the null hypothesis is not rejected, and 1 means the null hypothesis is rejected). Note that, within each plot and basin, points have been randomly displaced left and right to aid legibility.

Citation: Journal of Climate 34, 4; 10.1175/JCLI-D-20-0309.1

The similarity of Amazon and Óbidos residuals in Fig. 2 suggests that the assumption of RAmazon = 1.25 × RÓbidos is not grossly inappropriate. However, mean residuals and counts of significant distribution differences are generally slightly larger for the Amazon basin than the Óbidos catchment. This likely reflects a small error introduced by this assumption, as there is no clear reason why the other water cycle components should have consistently larger errors for the Amazon basin than the Óbidos catchment.

The ensemble means (either PEG_Ens or CHG_Ens) consistently give larger magnitude of residuals and larger counts of significant differences than several combinations using single datasets for each term, confirming the result seen in Fig. 1.

It is interesting to note that there is a general, although not exact, correspondence between mean residual and t-test significance count; a larger mean residual is usually accompanied by more months or seasons with significant differences between R and R^. (The fact that this correspondence is not exact reflects differences between seasonal bias patterns for different datasets.) An example of this fact is that for Óbidos catchment at monthly time scale, PEG_ERA5_ERA5_JPL has the smallest magnitude of mean residual and is one of only two combinations with no significant difference between R and R^ for any month (the other is CHG_ERA5_ERA5_JPL). Interestingly, at seasonal time scales, these combinations have significant differences for two seasons, while at annual time scales their differences are not significant for the Óbidos catchment but are for the Amazon basin. The disparity between seasonal and monthly counts of significant differences seems slightly puzzling. The explanation may lie in the fact that monthly R^ inherits relatively large noise from the GRACE retrievals, so has larger variance than R (not shown). At seasonal time scales, some of this noise has been smoothed out, so R^ has similar variance to R. This means that a particular difference (R^−R) could be significant at seasonal but not significant at monthly time scales.

Correlations between observed (R) and estimated discharge (R^) are shown in Fig. 3. At this point, we stress again that the observed discharge for the Amazon uses RAmazon = 1.25 × RÓbidos. Before discussing the correlation values, we note two important features of some of the discharge estimates (R^): 1) some combinations give negative R^ values for some months and seasons, which is clearly unphysical; and 2) some combinations give some months and seasons with the ratio R^Amazon/R^Óbidos<1, again physically unrealistic, despite having the ratios for all other water budget terms (e.g., PAmazon/PÓbidos) greater than 1. Despite these undesirable features, we continue with the analysis to investigate R^ variability.

Fig. 3.
Fig. 3.

Correlation coefficients at (left) monthly, (center) seasonal, and (right) annual time scales between discharge observed at Óbidos (multiplied by 1.25 for the Amazon, although this does not affect the correlation) and discharge estimated from water balance: R^. Each point represents one combination of water budget terms: some are highlighted, as shown in the legend. Note that, within each plot and basin, points have been randomly displaced left and right to aid legibility.

Citation: Journal of Climate 34, 4; 10.1175/JCLI-D-20-0309.1

The highest correlations are at seasonal time scales, likely because this averages out some of the month-to-month noise in the GRACE (and other) data but still retains a strong seasonal cycle, which boosts correlation values. The high seasonal correlations (almost all above 0.8; most above 0.9) suggests that most R^ combinations capture the correct seasonal cycle, despite the large biases in absolute value implied by Fig. 2. The low annual correlation coefficients (several below 0.4 and a few below 0.2) for some combinations suggests that they essentially do not capture interannual variability. The combinations with lowest annual correlation tend to use CMAP or MERRA-2 for precipitation and/or CLM or Noah for evapotranspiration. Some of these datasets have relatively high correlations at monthly and seasonal time scales, suggesting that they capture the seasonal cycle well despite not capturing interannual variability (which is smaller than the seasonal cycle range).

Ensemble means are again not generally the best performing combinations in this metric, with the exception that for annual time scales in the Óbidos catchment, CHG_Ens has the highest correlation coefficient. The combination with the smallest mean residual (PEG_ERA5_ERA5_JPL) from Fig. 2 has correlation coefficients about as high as (or higher than) CHG_Ens and PEG_Ens at monthly and annual time scales. It also has high correlation coefficients at seasonal time scales, but so do most other combinations, so it does not stand out in this respect.

As in Fig. 2, there is not a clear difference between Amazon basin and Óbidos catchment correlations in Fig. 3, although it appears that seasonal correlation coefficients are slightly higher for the Óbidos catchment than the Amazon basin. Nonetheless, we put slightly more stock in the correlations for the Óbidos catchment than for the Amazon basin, as it has a direct discharge measurement. PEG_CHIRPS_ERA5_JPL has the highest Óbidos correlation at both monthly and seasonal time scales, while at annual time scales CHG_Ens has very slightly higher correlation. It should be noted that PEG_CHIRPS_ERA5_JPL has mean residuals ~15%–20% of annual mean discharge and significant differences between R and R^ in 9 out of 12 months. This combination therefore appears to have good representation of water cycle variability despite significant biases in mean values.

4. Ocean salinity

We next look to ocean salinity as a consistency check on our results so far, asking first whether correlation between discharge and ocean salinity can differentiate between water cycle data combinations. Correlation coefficients between seasonal time series of R^ and ocean salinity near the mouth of the Amazon are shown in Fig. 4. Using monthly, instead of seasonal, time series results in lower magnitude correlation coefficients, but most of the conclusions drawn below still apply: in particular, discharge–salinity correlation magnitudes are higher at lag 0 than at lags of 1 or 2 months, suggesting that we are not distorting results by ignoring lags between 0 seasons and 1 season. Note that we expect negative correlation coefficients as greater discharge should cause lower salinity.

Fig. 4.
Fig. 4.

Correlation coefficients for seasonal time series of ocean salinity (using SMOS data) near the mouth of the Amazon (0°–3°N, 46.5°–52.5°W; see green boxes in Fig. 5) and discharge observed at Óbidos (light blue circle) and estimated from water balance using different combinations of data (small black points; several highlighted as shown in legend). Also shown are correlation coefficients between ocean salinity and, respectively, Amazon basin mean GPCP precipitation (red circle), Amazon basin mean CMAP precipitation (yellow circle), and P − E from the salinity region (purple circle; “P-E_local” in the legend). (left) Absolute values for all datasets; (right) anomalies from the seasonal cycle. In both panels, correlation coefficients are shown for lag-0 and lag-1 (salinity lags the other quantity by 1 season). Note that, within each plot and time lag, points have been randomly displaced left and right to aid legibility.

Citation: Journal of Climate 34, 4; 10.1175/JCLI-D-20-0309.1

The R^ values from most data combinations have larger magnitude (lag 0) correlation coefficients with salinity than do the Óbidos observation data. This is true for anomaly time series as well as absolute. Therefore we suggest that R^ captures both the mean annual cycle (absolute correlations) and interannual variability (anomaly correlations) better than the Óbidos observations. The combination with the highest magnitude of correlation coefficient for absolute time series is PEG_ERA5_Noah_JPL, while for the anomaly time series it is PEG_CHIRPS_Noah_JPL. The combinations highlighted in the previous section—PEG_CHIRPS_ERA5_JPL and PEG_ERA5_ERA5_JPL—also have relatively high magnitude correlation coefficients (although the anomaly correlation for PEG_ERA5_ERA5_JPL is only slightly higher than that of Óbidos observations).

Local P − E (i.e., the balance of precipitation and evaporation for the ocean region over which we consider salinity variation) has greater magnitude of (lag 0, absolute) correlation than Óbidos discharge and some of the R^ time series. Thus we cannot rule out that some of the salinity variability is controlled by local processes and not by discharge. Separating these factors is made difficult by closely related seasonal cycles of precipitation over this part of the ocean and over the Amazon. However, comparing the magnitudes (in terms of water volume per month) of discharge and P − E over the ocean region in question suggests that discharge is an order of magnitude larger, and therefore it seems likely that discharge dominates.

Amazon basin mean precipitation (shown in Fig. 4 from GPCP and CMAP) has almost as large magnitude correlation coefficients at 1-season lag as any of the discharge estimates do at lag 0. This is true for both absolute and anomaly time series. This suggests that precipitation variability drives discharge variability, with a time delay due to water transit times through the basin.

The large differences in Fig. 4 between the correlation coefficients for Óbidos observed discharge and a number of R^ estimates raise the possibility that the apparent pattern of discharge influence on wider tropical Atlantic salinity is sensitive to the discharge estimate used. To explore this further, Fig. 5 shows maps of correlation coefficients between SMOS salinity and three discharge estimates. There are a few features common to the three discharge estimates. In particular, for lag 0, all three discharge estimates have a region of high magnitude correlation along the Brazilian coast heading north and west from the Amazon mouth. This encompasses the region used in Fig. 4.

Fig. 5.
Fig. 5.

Maps of anomaly correlation coefficients between seasonal time series of ocean salinity (from SMOS) and several discharge estimates: (left) Óbidos observation, (center) PEG_GPCP_ERA5_JPL, and (right) PEG_ERA5_ERA5_JPL. Correlation coefficients are shown for (top) lags of 0, and salinity lagging discharge by (middle) 1 season and (bottom) 2 seasons. Nonsignificant values are masked out. The green rectangles near the mouth of the Amazon represent the area over which salinity (ocean grid points only) is averaged for correlations in Fig. 4.

Citation: Journal of Climate 34, 4; 10.1175/JCLI-D-20-0309.1

Conversely, other regions have marked difference in correlation patterns between the three discharge estimates. Some are likely not causally related, but some correspond to known features of the Amazon plume and therefore may indicate a causal link. First, we consider, in Fig. 5e, a stripe of relatively large magnitude correlation coefficients in the region 5°–10°N, 20°–45°W that appears to be related to the North Equatorial Countercurrent, which is known to contain Amazon plume water (e.g., Coles et al. 2013). This feature is apparent for PEG_GPCP_ERA5_JPL but not for the Óbidos observation or PEG_ERA5_ERA5_JPL. Second, in Fig. 5h, a region of relatively large magnitude correlation coefficients to the east of the Greater Antilles (15°–30°N, 50°–60°W) may correspond to the Amazon plume’s Northern Extension Region defined by Fournier et al. (2017). This feature is weakly present in Figs. 5g and 5i, but is more extensive and contains larger magnitude correlation coefficients in Fig. 5h. These two features suggest that conclusions drawn about the effect of Amazon discharge variability on ocean variability may depend on the choice of discharge estimate. This has been noted by Salisbury et al. (2011) but not widely appreciated in other oceanographic studies of the Amazon plume.

5. Discussion and conclusions

We have used a range of remote sensing and reanalysis datasets to investigate the water cycle of the Amazon basin. There is considerable spread in basin-averaged precipitation and evapotranspiration among the datasets. For changes in terrestrial water storage, the spread among three widely used GRACE satellite retrievals is relatively small. However, this is likely due to the fact that all three use the same underlying data, and so do not fully sample the same kind of systematic uncertainties as the precipitation and evapotranspiration datasets. For river discharge, the observation at Óbidos is thought to have a relatively low error compared to other quantities. However, we find evidence that a commonly used approach to scale the Óbidos observation to represent the entire Amazon discharge may misrepresent the true seasonal cycle.

The water budget of the Amazon basin can be closed with some, but not all, combinations of datasets. Notably, using ensemble means from several precipitation and evapotranspiration datasets results in a large mean residual (approaching 50% annual mean discharge). Several combinations of individual datasets give much smaller closure residuals.

Comparing observed discharge at Óbidos to discharge estimated from water balance (i.e., R^) gives high magnitude correlations (~0.8–1.0) for all data combinations at seasonal time scales, while at annual time scales some combinations have much lower magnitude correlations (~0.2–0.9). The seasonal correlations suggest that some datasets capture the seasonal cycle of water balance quite well, despite large mean biases (shown by closure residuals) and/or poor representation of interannual variability (shown by annual correlations). Estimating discharge from water balance also has the undesirable property that discharge for the entire Amazon is sometimes predicted to be smaller than that for Óbidos. Of even more concern is that, for some data combinations, negative discharge is occasionally predicted. This is obviously unphysical, at least on the large scale of the Amazon basin. Mathematically, negative discharge values are mostly a sign of mean-state biases in the underlying quantities (precipitation, evapotranspiration, etc.). Given that most data combinations have negative closure residuals (Fig. 2), negative discharge values are least common (or do not occur at all) in the combinations with smallest magnitude of closure residual.

A further consistency check is based on the ocean salinity around the mouth of the Amazon, based on the assumption that this is strongly controlled by the river discharge. Many of the water balance estimates of discharge have larger magnitude correlation coefficients (both absolute and anomaly) with salinity than does the Óbidos observation data. This suggests that using the Óbidos discharge to represent the discharge from the entire basin misrepresents some important aspects of the seasonal cycle and variability.

The analyses discussed above essentially are a set of independent tests for a self-consistent picture of the water cycle. Given our conclusions that ensemble means do not generally perform better than individual combinations, it is reasonable to ask whether any single data combination consistently performs well across all tests.

  1. The requirement of closure (and associated requirement for good agreement between distributions of R and R^) rules out the lower precipitation (especially CMAP and MERRA-2) and higher evapotranspiration (especially GLEAM and MERRA-2) estimates. The lowest residual is found with ERA5 precipitation and evapotranspiration, but CHIRPS and GPCP precipitation estimates are also viable if combined with the lowest evapotranspiration estimate (CLM).

  2. The requirement for realistic water budget-based estimates of discharge (i.e., R^)—including high correlation with observed discharge at Óbidos and nonnegative values—also provides further differentiation between data combinations. PEG_CHIRPS_ERA5_JPL has the highest correlations at monthly and seasonal time scales, and very close to the highest at annual time scales. However, it has significant closure residuals and occasional negative values. The combination with smallest mean closure residual, PEG_ERA5_ERA5_JPL, has relatively high correlations for all three time scales and no negative values. Some rather low correlations at annual time scales cast doubt on the ability of CMAP and MERRA-2 precipitation and CLM and Noah evapotranspiration to portray interannual variability.

  3. The requirement for good agreement with ocean salinity variability suggests that many combinations provide a more accurate portrayal of Amazon discharge seasonality than Óbidos observed discharge. In terms of correlations of absolute values, PEG_ERA5_ERA5_JPL is again very close to the highest magnitude (−0.94, versus −0.96 for PEG_ERA5_Noah_JPL). For anomalies however, it is more significantly different from the largest magnitude correlation (−0.50, vs −0.65 for PEG_CHIRPS_Noah_JPL).

This discussion highlights that no single data combination performs best in all metrics. However, we suggest that PEG_ERA5_ERA5_JPL provides the best compromise across the metrics (along with CHG_ERA5_ERA5_JPL, which is generally quite similar). This does not mean we are arguing that this combination of datasets is uniquely able to tell us about the water cycle processes in the Amazon. We advocate continued use of multiple datasets to study water cycle processes: in the absence of detailed error estimates, based on in situ measurements and appropriate statistical models, such an approach is a useful way to understand uncertainties. Nonetheless, our closure results provide an important constraint: that mean precipitation over the Amazon is at the top end of current estimates and evapotranspiration is at the lower end of current estimates. This gives important insights into not only precipitation and evapotranspiration, but also their ratio: E/P being at the lower end of possible estimates has implications for understanding moisture transport and recycling over the Amazon basin (Eltahir and Bras 1994; Rocha et al. 2018) and surrounding regions. Further, in situations where consistency among water cycle components is important (e.g., model validation), the combinations noted are likely the best choices, and ensemble mean quantities should be used with caution.

It is worth asking at this point what lessons our results provide for development of observation-based datasets, models, and reanalyses. For precipitation, we suggest that it is important to have sufficient resolution (in models and gridded datasets) to capture high precipitation over complex terrain of the Andes mountains (Fig. S1). CMAP and GPCP do not have sufficient resolution, and MERRA-2 corrected precipitation has a similar pattern to these two. The higher-resolution datasets—CHIRPS, ERA5, and MERRA-2 raw precipitation—do show local maxima over the Andes. The MERRA-2 raw precipitation over the Andes seems quite excessive, which is a sign that global models (including those used in reanalyses) may continue to have difficulty representing precipitation in complex terrain. MERRA-2’s excessive precipitation may also be a sign of overactive moisture cycling and related biases introduced by analysis increments (Trenberth et al. 2011; Seager and Henderson 2013).

Evapotranspiration continues to show large differences between datasets [in agreement with earlier studies (e.g., Getirana et al. 2014)], reflecting difficulties in modeling surface–groundwater interactions (Miguez-Macho and Fan 2012) and canopy processes (Wu et al. 2016). Our results do show some encouraging signs of progress, however, in the consistency and realism of reanalysis precipitation and evapotranspiration: it has been found in past studies that inferring P − E from moisture convergence is more reliable than taking P and E directly from a reanalysis (e.g., Trenberth and Fasullo 2013). Indeed, the MERRA-2 excessive raw precipitation, noted above, is an example of this. In contrast, our results give indirect evidence that the two methods may be more similar in ERA5 than in past reanalyses.

Our analysis has shown problems with using Óbidos discharge to represent discharge from the entire Amazon. This has consequences that can affect both terrestrial and oceanographic studies of the Amazon. However, our analysis also suggests a simple method to alleviate this issue. The method of Dai et al. (2009) is essentially RAmazon = k × RÓbidos with a constant k. We suggest that the main problem with this method is that it misrepresents the Amazon seasonal cycle, and so a seasonally varying k is a simple alternative. The seasonal cycle of k can be calculated for any data combination, and we show the seasonal cycle (and interannual variability) for three combinations in Fig. 6. The spread among datasets and interannual variability are large for much of the year (roughly October through April). However, there is relatively good consensus that the ratio k is significantly smaller than 1.25 from June through September. Changing k in these four months to 1.15 (chosen subjectively from data in Fig. 6) increases the magnitudes of monthly and seasonal correlation coefficients (with near-river-mouth salinity) from −0.72 to −0.79, or roughly a 10% increase in variance explained (this is based on absolute values; anomaly correlation coefficients change relatively little).

Fig. 6.
Fig. 6.

Mean annual cycle of ratio of discharge for Amazon basin vs Óbidos catchment for three data combinations and the constant value from Dai et al. (2009). Shading shows interannual standard deviation around the mean.

Citation: Journal of Climate 34, 4; 10.1175/JCLI-D-20-0309.1

Note that we do not use all available datasets for each component in this study for various reasons: some of the newly developed datasets (e.g., land evapotranspiration) do not cover enough of the time period studied here (in particular they may have little overlap with GRACE satellite data); the number of combinations would increase substantially, making it difficult to present and discuss some of the results (e.g., in Figs. 2–4); and our conclusions are unlikely to be much affected by the increased number of products for each component.

Acknowledgments

This work was supported by NASA (under Grants NNX14AM02G and NNX16AN37G) and the U.S. Department of Energy (under Grants DE-SC0016533 and DE-AC52-07NA27344/B639244). We thank Chris Castro and Ali Behrangi for useful discussions of our ideas and results. We thank the editor, Benjamin Lintner, and four anonymous reviewers for their constructive comments.

Data availability statement

All data used in this study are freely and publicly available. Data sources are given as citations in the text. The computer code used for our data analysis is publicly available at https://bitbucket.org/jack_eyre/amazon_12_august_2020.

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  • <sc>Fig</sc>. 1.
    View in gallery
    Fig. 1.

    Mean annual cycles of Amazon basin water cycle components: precipitation (cyan), evapotranspiration (pink), change in terrestrial water storage (purple), discharge (black), and the closure residual (yellow). For precipitation, evapotranspiration, and terrestrial water storage change, the thick line shows the ensemble mean and shading represents the ensemble spread (maximum to minimum). The discharge for the entire Amazon basin is estimated using Óbidos discharge multiplied by 1.25 (following Dai et al. 2009). Water budget closure residuals are shown for two combinations: one (solid line; referred to as PEG_Ens) uses the ensemble means of precipitation, evapotranspiration. and terrestrial water storage change, while the other (dashed line; referred to as PEG_ERA5_ERA5_JPL) uses ERA5 precipitation and evapotranspiration and JPL terrestrial water storage change.

  • <sc>Fig</sc>. 2.
    View in gallery
    Fig. 2.

    Mean residuals of water budgets for Óbidos catchment area and entire Amazon basin at (left) monthly, (center) seasonal, and (right) annual time scales, expressed as a fraction of annual mean discharge. Residuals for Amazon catchment use Óbidos discharge multiplied by 1.25. Each point represents one combination of water budget terms (e.g., PEG_ERA5_ERA5_JPL). For monthly and seasonal panels, points are colored according to the count of months or seasons (respectively) that result in a significant difference between discharge R and R^, based on Welch’s (unequal variance) t test with a significance level α = 0.05. For the annual plot, points are colored according to whether the distribution of annual means differ according to the same test (for a null hypothesis that the distributions are the same, 0 means the null hypothesis is not rejected, and 1 means the null hypothesis is rejected). Note that, within each plot and basin, points have been randomly displaced left and right to aid legibility.

  • <sc>Fig</sc>. 3.
    View in gallery
    Fig. 3.

    Correlation coefficients at (left) monthly, (center) seasonal, and (right) annual time scales between discharge observed at Óbidos (multiplied by 1.25 for the Amazon, although this does not affect the correlation) and discharge estimated from water balance: R^. Each point represents one combination of water budget terms: some are highlighted, as shown in the legend. Note that, within each plot and basin, points have been randomly displaced left and right to aid legibility.

  • <sc>Fig</sc>. 4.
    View in gallery
    Fig. 4.

    Correlation coefficients for seasonal time series of ocean salinity (using SMOS data) near the mouth of the Amazon (0°–3°N, 46.5°–52.5°W; see green boxes in Fig. 5) and discharge observed at Óbidos (light blue circle) and estimated from water balance using different combinations of data (small black points; several highlighted as shown in legend). Also shown are correlation coefficients between ocean salinity and, respectively, Amazon basin mean GPCP precipitation (red circle), Amazon basin mean CMAP precipitation (yellow circle), and P − E from the salinity region (purple circle; “P-E_local” in the legend). (left) Absolute values for all datasets; (right) anomalies from the seasonal cycle. In both panels, correlation coefficients are shown for lag-0 and lag-1 (salinity lags the other quantity by 1 season). Note that, within each plot and time lag, points have been randomly displaced left and right to aid legibility.

  • <sc>Fig</sc>. 5.
    View in gallery
    Fig. 5.

    Maps of anomaly correlation coefficients between seasonal time series of ocean salinity (from SMOS) and several discharge estimates: (left) Óbidos observation, (center) PEG_GPCP_ERA5_JPL, and (right) PEG_ERA5_ERA5_JPL. Correlation coefficients are shown for (top) lags of 0, and salinity lagging discharge by (middle) 1 season and (bottom) 2 seasons. Nonsignificant values are masked out. The green rectangles near the mouth of the Amazon represent the area over which salinity (ocean grid points only) is averaged for correlations in Fig. 4.

  • <sc>Fig</sc>. 6.
    View in gallery
    Fig. 6.

    Mean annual cycle of ratio of discharge for Amazon basin vs Óbidos catchment for three data combinations and the constant value from Dai et al. (2009). Shading shows interannual standard deviation around the mean.

Fig. 1.

Mean annual cycles of Amazon basin water cycle components: precipitation (cyan), evapotranspiration (pink), change in terrestrial water storage (purple), discharge (black), and the closure residual (yellow). For precipitation, evapotranspiration, and terrestrial water storage change, the thick line shows the ensemble mean and shading represents the ensemble spread (maximum to minimum). The discharge for the entire Amazon basin is estimated using Óbidos discharge multiplied by 1.25 (following Dai et al. 2009). Water budget closure residuals are shown for two combinations: one (solid line; referred to as PEG_Ens) uses the ensemble means of precipitation, evapotranspiration. and terrestrial water storage change, while the other (dashed line; referred to as PEG_ERA5_ERA5_JPL) uses ERA5 precipitation and evapotranspiration and JPL terrestrial water storage change.
Fig. 2.

Mean residuals of water budgets for Óbidos catchment area and entire Amazon basin at (left) monthly, (center) seasonal, and (right) annual time scales, expressed as a fraction of annual mean discharge. Residuals for Amazon catchment use Óbidos discharge multiplied by 1.25. Each point represents one combination of water budget terms (e.g., PEG_ERA5_ERA5_JPL). For monthly and seasonal panels, points are colored according to the count of months or seasons (respectively) that result in a significant difference between discharge R and R^, based on Welch’s (unequal variance) t test with a significance level α = 0.05. For the annual plot, points are colored according to whether the distribution of annual means differ according to the same test (for a null hypothesis that the distributions are the same, 0 means the null hypothesis is not rejected, and 1 means the null hypothesis is rejected). Note that, within each plot and basin, points have been randomly displaced left and right to aid legibility.
Fig. 3.

Correlation coefficients at (left) monthly, (center) seasonal, and (right) annual time scales between discharge observed at Óbidos (multiplied by 1.25 for the Amazon, although this does not affect the correlation) and discharge estimated from water balance: R^. Each point represents one combination of water budget terms: some are highlighted, as shown in the legend. Note that, within each plot and basin, points have been randomly displaced left and right to aid legibility.
Fig. 4.

Correlation coefficients for seasonal time series of ocean salinity (using SMOS data) near the mouth of the Amazon (0°–3°N, 46.5°–52.5°W; see green boxes in Fig. 5) and discharge observed at Óbidos (light blue circle) and estimated from water balance using different combinations of data (small black points; several highlighted as shown in legend). Also shown are correlation coefficients between ocean salinity and, respectively, Amazon basin mean GPCP precipitation (red circle), Amazon basin mean CMAP precipitation (yellow circle), and P − E from the salinity region (purple circle; “P-E_local” in the legend). (left) Absolute values for all datasets; (right) anomalies from the seasonal cycle. In both panels, correlation coefficients are shown for lag-0 and lag-1 (salinity lags the other quantity by 1 season). Note that, within each plot and time lag, points have been randomly displaced left and right to aid legibility.
Fig. 5.

Maps of anomaly correlation coefficients between seasonal time series of ocean salinity (from SMOS) and several discharge estimates: (left) Óbidos observation, (center) PEG_GPCP_ERA5_JPL, and (right) PEG_ERA5_ERA5_JPL. Correlation coefficients are shown for (top) lags of 0, and salinity lagging discharge by (middle) 1 season and (bottom) 2 seasons. Nonsignificant values are masked out. The green rectangles near the mouth of the Amazon represent the area over which salinity (ocean grid points only) is averaged for correlations in Fig. 4.
Fig. 6.

Mean annual cycle of ratio of discharge for Amazon basin vs Óbidos catchment for three data combinations and the constant value from Dai et al. (2009). Shading shows interannual standard deviation around the mean.
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