Interactive comment on “ On the importance of cascading moisture recycling in South America ”

1. On the Relevance of the Paper: Rather than a study of marginal interest, appealing to a particular subset of readers interested in moisture dynamics over a particular region, we are in the presence of a study with much broader relevance, not least given the applicability of the methodologies to other scientific problems in Atmospheric Chemistry and Physics. Having said that, the topical problem of moisture recycling in South America is itself a fascinating problem,


Introduction
Continental moisture recycling, the process by which evapotranspiration from the continent returns as precipitation to 35 the continent (Brubaker et al., 1993;Eltahir and Bras, 1994;van der Ent et al., 2010) is particularly important for the South American hydrological cycle.In the Amazon basin, between 25 and 35 % of the moisture is regionally recycled (Eltahir and Bras, 1994;Trenberth, 1999;Bosilovich and 40 Chern, 2006;Burde et al., 2006;Dirmeyer et al., 2009).Particularly during the wet season, the moisture from the Amazon basin is also exported out of the basin, transported via the South American Low Level Jet (SALLJ) along the Andes and contributes to precipitation over the La Plata basin (Marengo,45 2005; Drumond et al., 2008Drumond et al., , 2014;;Arraut and Satyamurty, 2009;Dirmeyer et al., 2009;van der Ent et al., 2010;Arraut et al., 2012;Martinez et al., 2014).
Land-use change -in particular deforestation in the Amazon basin -alters the evapotranspiration rate and affects the 50 water cycle (see review in Marengo, 2006).A resulting reduction in regional moisture supply may have important consequences for the stability of Amazon rainforests (Oyama and Nobre, 2003;Cox et al., 2004;Betts et al., 2004;Hirota et al., 2011;Knox et al., 2011;Spracklen et al., 2012).
Rainfall reduction in the La Plata basin may have negative effects on rainfed agriculture (Rockström et al., 2009;Keys et al., 2012).Even if regional impact of changes in precipitation patterns from deforestation has been intensively studied using simulations from atmospheric general circulation models with deforestation scenarios (Lean and Warrilow, 1989;Shukla et al., 1990;Nobre et al., 1991Nobre et al., , 2009;;Werth and Avissar, 2002;Sampaio et al., 2007;Da Silva et al., 2008;Hasler et al., 2009;Walker et al., 2009;Medvigy et al., 2011;Bagley et al., 2014) the magnitude of rainfall reduction and the location of the most affected regions are still uncertain.In order to improve predictability of rainfall changes with future land-use and climate change, further advancement in our understanding of continental moisture recycling in South America is needed.
To identify the sources and sinks of continental moisture and to quantify regional and continental moisture recycling rates in South America, several methods have been used including isotopes (Salati et al., 1979;Gat and Matsui, 1991;Victoria et al., 1991), atmospheric bulk models (Brubaker et al., 1993;Eltahir and Bras, 1994;Trenberth, 1999;Burde et al., 2006) and quasi-isentropic back-trajectory method (Dirmeyer et al., 2009;Spracklen et al., 2012;Bagley et al., 2014).In addition, numerical atmospheric moisture tracking experiment allows to identify the spatial distribution of evapotranspiration from a specific region.It has been performed online with a general circulation model (GCM) (Bosilovich and Chern, 2006) or a posteriori (offline) with reanalysis data (Sudradjat et al., 2002;van der Ent et al., 2010;Keys et al., 2012) (see a review of the methods in van der Ent et al., 2013;Burde and Zangvil, 2001).
In most of the previous atmospheric moisture tracking studies, moisture from a group of grid cells covering a region of interest (typically the continent) is tracked simultaneously until it returns to the land surface as precipitation or leaves the domain.This approach is useful to investigate how evapotranspiration from a specific location is transported in the atmosphere and precipitates at first in another location.However, precipitating moisture can be re-evapotranspirated in the same location (re-evaporation cycle) and can be transported further downwind before it falls again as precipitation over land.In most of the previous studies, only moisture recycling with no intervening re-evaporation cycles ("Direct Moisture Recycling, DMR") is considered.Here, we track moisture evaporating from each grid cell within a larger the domain (i.e., the South American continent) individually.By doing so, we are able to diagnose for each grid cell the amount of evaporating moisture that precipitates in any other cell, i.e., to build a moisture recycling network.Such an approach enables us to study the DMR between important subregions of the South American continent (e.g., the Amazon and the La Plata Basin), but also the moisture transport that involves at least one re-evaporation cycle ("cascading moisture recycling, CMR").
While only a few previous studies deal with the impor-110 tance of CMR (Numaguti, 1999;Goessling and Reick, 2013), these studies are based on general circulation models rather than on observation-based data.In the following, we quantify the importance of CMR for the regional climate in South America using numerical atmospheric moisture tracking a 115 posteriori with historical climatological datasets.Our analysis is based on precipitation, evapotranspiration, wind and humidity datasets from a combination of observation-based, reanalysis and merged synthesis products (average of several existing products). 120 Our network-based approach allows us to apply analysis methods developed in complex network theory to improve our understanding of moisture recycling pathways in South America.The potential of complex network based analysis of the climate system has been shown in a range of applica-125 tions such as the detection of teleconnections (Tsonis et al., 2008;Donges et al., 2009a,b), the propagation of extreme events (Malik et al., 2012;Boers et al., 2013) and the El Niño forecasting (Ludescher et al., 2013).While previous network based studies rely on statistical analysis in the network con-130 struction, our approach is based on a flux-based network, which represents a substantial methodological advancement.
In this study we focus on three key questions: 1. what is the importance of CMR in South America and in particular for the moisture transport from the Amazon 135 basin towards the La Plata basin?
2. Which are the important intermediary regions for the transport of moisture from sources and sinks on the continent?
3. Which are the key regions where the pathways of CMR 140 are channeled?
In Sect.2.1 we describe the tagged water experiment using the WAM-2layers and we explain how we use it to build moisture recycling networks.We explain the assumptions made in the proposed analysis in Sect.2.2.We develop new 145 measures in Sects.2.3 and 2.4 and we present the complex network analysis in Sect.2.5.An explanation of the complementarity of the measures is presented in Sect.2.6.After comparing the continental and regional recycling ratios with other existing studies in Sect.3.1, we present and discuss new 150 results on the importance of CMR in Sect.3.2 and on complex network analysis in Sect.3.3.We present an in-depth analysis of the moisture recycling between the Amazon basin and the La Plata basin in Sect.3.4.Finally, we warn against possible effects of land-use change in the intermediary re- The WAM-2layers runs on a 1.5 • longitude/latitude grid.Because the local moisture recycling (re-evaporation cycles) is scale-dependent, the amount of locally recycled moisture 180 within a grid cell depends on the spatial resolution of the model (van der Ent and Savenije, 2011, Fig. 4).However, in our study, the re-evaporation cycles are occurring along the pathway of moisture recycling.Since we are integrating over all pathways contributing to the large-scale moisture transport, the spatial resolution has little influence on our results.The typical length scale of direct links in moisture recycling is larger than 1000 km (c.a. 9 • ) in the region (van der Ent and Savenije, 2011, Fig. 5), which indicates that our resolution is sufficient to analyze the processes of interest.
We omitted the first year of the considered period from the results because of model spin-up.The output are aggregated first to monthly, then to seasonally average imports and exports between all land grid cells.This temporal resolution is reasonable for our purpose since the time scale of moisture recycling does not exceed 30 days in the studied region (van der Ent and Savenije, 2011, Fig. 5).
These seasonal averages are used to build two seasonal moisture recycling networks, which are assumed to be static for the whole season.This implies that in the proposed anal-200 ysis, for each season moisture is tracked forward and backward in space but not in time.

Input of WAM-2layers
In order to reduce the uncertainty associated with the input data, we used two different datasets as input for WAM-205 2layers (that we call "input MOD" and "input LFE", see Table 1).The input MOD covers the period 2000 -2010 and contains 3 hourly precipitation estimates from the Tropical Rainfall Measuring Mission (TRMM) based on the algorithm 3B-42 (version 7) (Huffman et al., 2007) and 8 days evapo-210 transpiration estimates from Moderate Resolution Imaging Spectroradiometer (MODIS) based on the MOD16 ET algorithm (Mu et al., 2011).Precipitation dataset from TRMM are considered to be reliable over South America and in particular in the Amazon basin where others products perform 215 poorly due to the lack of ground based measurements (Franchito et al., 2009;Rozante et al., 2010).TRMM precipitation data are shown to represent high frequency variability sufficiently well (Kim and Alexander, 2013).However, it is systematically biased during the dry season in the northeast-220 ern coast of Brazil, where precipitation is underestimated (Franchito et al., 2009) and at the junction of Argentina, Paraguay and Brazil, where it is overestimated (Rozante and Cavalcanti, 2008).Evapotranspiration from MODIS is estimated using the Penman-Monteith equation (Monteith et al., 225 1965) forced by satellite and meteorological reanalysis data.Like other "observation-based" evapotranspiration estimations, the quality of the MODIS dataset depends on the quality of the forcing data and the parameterization of the algorithm.The MODIS evapotranspiration dataset has been val-230 idated with 10 eddy flux towers located in the Amazonian region under various land cover types (Loarie et al., 2011;Ruhoff, 2011).
The input LFE covers the period 1989 -1995 and contains monthly evapotranspiration averaged from 39 differ-235 ent products (LandFlux-Eval, Mueller et al. (2013)), as well as monthly precipitation averaged from four different observation-based precipitation datasets: Climate Research Unit (CRU) (New et al., 2000), the Global Precipitation Climatology Centre (GPCC) (Huffman et al., 1995;Adler et al., 240 2003), the Global Precipitation Climatology Project (GPCP) (Adler et al., 2003) and the unified climate prediction center (CPC) from the National Oceanic and Atmospheric Administration (NOAA) (Chen et al., 2008).The four precipitation datasets are interpolations from rain gauge data (in combi-245 nation with satellite observation in the case of GPCC) and have been used as forcing dataset for the "observation-based" evapotranspiration product in LandFlux-Eval (Mueller et al., 2013).Here, we include the evapotranspiration products in LandFluxEval that are not only derived from observations, 250 but also calculated via land-surface models and output from reanalysis.
Both datasets are complemented by 6 hourly specific humidity and wind speed in three dimensions from the ERA-Interim reanalysis product (Dee et al., 2011) for the corre-255 sponding periods.Because these two variables are used to get the horizontal moisture fluxes, the choice of the reanalysis product matters for the eventual results of the WAM-2layers (Keys et al., 2014).Humidity estimation has been improved in the ERA-Interim product in comparison with others re-260 analysis products (Dee and Uppala, 2008).
The temporal resolution of the input data needed in WAM-2layers is 3 hours.Therefore, we downscaled the input MOD and LFE based on the temporal dynamic found in the ERA-Interim evapotranspiration and precipitation products.In addition, all data is downscaled to 0.5 h as requested by the numerical scheme of WAM-2layers.All data is upscaled to a regular grid of 1.5 • longitude/latitude and covers the South American continent to 50 • S, which is the southernmost latitude covered by TRMM product.
The long term seasonal average of evapotranspiration and precipitation as well as moisture flux divergence (evapotranspiration -precipitation) are shown in Figs. 1 and 2. The high rainfall in the South Atlantic Convergence Zone (including the Amazon basin, central and south-eastern Brazil) during the wet season (December to March) compared to the dry season (June to September) characterizes the South American Monsoon System (SAMS) (Liebman et al., 1999;Grimm et al., 2004;Arraut and Satyamurty, 2009).
The evapotranspiration and precipitation in the input MOD have an overall positive bias compared to the input LFE.
While the spatial patterns of evapotranspiration show good agreement on a continental scale, there are also several distinct differences.In particular the wet season evapotranspiration in the sub-tropical South America is much weaker in the input MOD then LFE.Interpreting and explaining the differences between the datasets is beyond the scope of this study.
For an evaluation of the different types of products (model calculation, "observation-based" and reanalysis), we refer to Mueller et al. (2011).
In both inputs the evapotranspiration exceeds the total precipitation in the southern part of the Amazon basin during the dry season, indicating that this region is a net source of moisture for the atmosphere (Fig. 1c and 2c).This is in agreement with previous studies demonstrating a maintaining of the greenness of the Amazon forests (Morton et al., 2014) and the absence of water stress during the dry season due to the deep root system, which enables the pumping of the water from the deeper water table (Nepstad et al., 1994;Miguez-Macho and Fan, 2012).
We find that, averaged over the full time period, evapotranspiration exceeds precipitation in northeastern Brazil and in the Atacama Desert in both datasets, as well as along the Andes in the input MOD.Possible explanations for the imbalance in these arid to semi-arid regions are irrigation or biases in the input data as mentioned above.As this might lead to a bias in moisture recycling ratios due to an overestimation of the contribution of evapotranspiration to local precipitation, we will exclude these grid cells from our analysis.

Construction of a complex network based on WAM-2layers
The output of WAM-2layers is a matrix M = {m ij } for all i, j ∈ N with N the number of grid cells in the continent (N = 681).The non-diagonal element m ij is the amount of evapotranspiration in grid cell i that precipitates in grid cell j and the diagonal element m ii is the amount of evapotran-spiration that precipitates in the same grid cell (locally recycled moisture).The output of WAM-2layers can be interpreted as the adjacency matrix of a directed and weighted complex network with self-interactions, where nodes of the 320 network represent continental grid cells and links between nodes represent the direction and amount of moisture transported between them (Fig. 3).

Basic assumptions
In order to track moisture forward or backward from a given 325 region Ω that can be of any shape and scale (grid cell, basin, continent), we assume that the moisture composition within the surface reservoir and the atmosphere for each grid cell remains the same.This implies that, in each grid cell, the tagged fraction of precipitation is linearly proportional to the 330 tagged fraction of evapotranspiration and the tagged fraction of transported moisture: where E is the total evapotranspiration, P is the total precipi-335 tation, m is the transported moisture towards or from another grid cell, P Ω is the tagged fraction of precipitation, E Ω is the tagged fraction of evapotranspiration and m Ω is the tagged fraction of transported moisture towards or from another grid cell.We call "tagged fraction" the share of the moisture orig-340 inating from Ω in the case of a backward tracking and the share of moisture precipitating over Ω in the case of a forward tracking.
This assumption is valid under two conditions: (1), evapotranspiration follows directly after the precipitation event 345 or (2), the fraction of tagged moisture in the surface reservoir and the atmosphere can be assumed to be temporally constant (i.e., in steady state) (Goessling and Reick, 2013).The first condition is usually fulfilled during interception and fast transpiration, which are important components of the to-350 tal evapotranspiration, particularly in warm climates and for shallow rooted plants (Savenije, 2004).However, in seasonal forests with deep rooted trees, the moisture that is evaporated during the dry season can be hold back for several months (Savenije, 2004).By analyzing a seasonally static moisture 355 recycling network, we account for this limitation.The second condition is fulfilled if the soil water at the beginning has the same composition (in term of tagged fraction) as the atmospheric moisture at the end of the season.

Moisture recycling ratio 360
Common measures to quantify the strength of the direct link between precipitation in a specific location and evapotranspiration from another location are the moisture recycling ratios (called hereafter DMR ratio) (Eltahir and Bras, 1994;Trenberth, 1999;Bosilovich and Chern, 2006;Dirmeyer et al., et al., 2014).The DMR ratios are only used to investigate DMR.Here, we further develop these measures in order to take CMR into account.

DMR (direct moisture recycling) ratios
Two kinds of DMR ratios have been developed in a previous study (van der Ent et al., 2010): the direct precipitation recycling ratio and the direct evapotranspiration recycling ratio.The direct precipitation recycling ratio ρ Ω has been defined as the fraction of precipitation that is originating from evapotranspiration from a defined region Ω with no intervening re-evaporation cycle.The ρ Ω for grid cell j is calculated as: where m ij is the amount of evapotranspiration in i that precipitates in j with no intervening re-evaporation cycle and P j is the precipitation in j.We note that ρ Ω averaged over all grid cells in Ω gives the regional recycling ratio, i.e, the fraction of precipitation that is regionally recycled (Eltahir and Bras, 1994;Burde et al., 2006; van der Ent and Savenije, downwind (Fig. 4).
Similarly, the direct evapotranspiration recycling ratio ε Ω has been defined as the fraction of evapotranspiration that falls as precipitation over a defined region Ω with no intervening re-evaporation cycle.The ε Ω for grid cell i is calculated as: where E i is the evapotranspiration in i. High values indicate the "direct source regions" of precipitation over Ω, i.e., the regions that contribute directly (i.e., through DMR) to rainfall over Ω.A direct source region distributes moisture towards Ω, which might be originating from further up-wind regions (Fig. 4).
If Ω is the entire South American continent, ε Ω becomes the continental evapotranspiration recycling ratio (ε c ) and ρ Ω the continental precipitation recycling ratios (ρ c ) as defined in van der Ent et al. (2010).Considered together, ε c and ρ c indicate respectively sources and sinks of continental moisture.In this study we neglect possible contributions of moisture in South America from and to other continents, since these contributions to the overall moisture budget are small (van der Ent et al., 2010, Table 2).

CMR (cascading moisture recycling) ratios
We define the cascading precipitation recycling ratio ρ casc Ω as the fraction of precipitation that is originating from evapo-transpiration from Ω and that has run through at least one reevaporation cycle on the way.High values indicate the "cascading sink regions" of evapotranspiration from Ω, i.e., the regions that are dependent on evapotranspiration coming in-420 directly (i.e., through CMR) from Ω for local precipitation.
A cascading sink region is the last destination of evapotranspiration from Ω before it is advected over the ocean (Fig. 4).
We also define the cascading evaporation recycling ratio 425 ε casc Ω as the fraction of evapotranspiration that falls as precipitation over Ω after at least one re-evaporation cycle on the way.High values indicate the "cascading source regions" of precipitation over Ω, i.e., the regions that contribute indirectly (i.e., through CMR) to rainfall over Ω.A cascading source region is the origin of moisture that is distributed from somewhere else towards Ω (Fig. 4).
The moisture inflow (resp.outflow) that crosses the border of Ω may be counted several times as it is involved in several pathways of CMR.To avoid this, we only track moisture that 435 crosses the border of Ω.This implies that we consider reevaporation cycles outside Ω only (Fig. 4).For a complete description of the methodology, we refer to Appendix B1.

Application to the Amazon basin and the La Plata basin 440
To study the moisture recycling between the Amazon basin (defined by the red boundaries in Fig. 1e) and the La Plata basin (defined by the purple boundaries in Fig. 1d), we use ρ Ω and ρ casc Ω with Ω being all grid cells covering the Amazon basin (ρ Am and ρ casc Am respectively) and ε Ω and ε casc Ω with

445
Ω being all grid cells covering the La Plata basin (ε Pl and ε casc Pl respectively).High values of ρ Am and ρ casc Am indicate together the sink regions of evapotranspiration from the Amazon basin and high values of ε Pl and ε casc Pl highlight source regions of precipitation over the La Plata basin (Fig. 4).

450
Considered together, the DMR ratios and the CMR ratios ratios provide a full picture of the source -sink relationship between the Amazon basin and the La Plata basin that is needed to estimate the effects of land-use change for downwind precipitation patterns.ρ casc Am and ρ Am quantify the local 455 dependency on incoming moisture from the Amazon basin (with and without re-evaporation cycles) and therefore the local vulnerability to deforestation in the Amazonian rainforests.Considering ρ Am only would lead to underestimation of this dependency.On the other hand, ε Pl and ε casc Pl provide 460 information on the upwind regions that contribute to rainfall over the La Plata basin and, consequently, that should be preserved from intensive land-use change in order to sustain water availability in the La Plata basin.

Quantifying CMR (cascading moisture recycling)
465 To quantify the importance of CMR for the total moisture inflow (precipitation, P ) and outflow (evapotranspiration, E), we cut-off all re-evaporation of moisture originating from the continent and we estimate the resulting reduction in total moisture inflow (∆P c ) and outflow (∆E c , see Appendix B3 for further information on the methodology).∆P c /P is the fraction of precipitation that comes from re-evaporation of moisture originating from the continent, i.e., that has been evaporated in at least two locations on the continent.In addition, we are interested in the importance of reevaporation cycles that are occurring in the intermediary re-485 gions for the total moisture in-and outflow.We use the same approach as above.We cut-off all re-evaporation in the intermediary region of moisture originating from the continent and we estimate the resulting reduction in total moisture inflow (∆P m ) (see Appendix B3).∆P m /P is the fraction of total moisture inflow that comes from CMR in the intermediary region (i.e., that has run through at least one reevaporation cycle in the intermediary region).It quantifies the dependency on CMR in the intermediary region for local rainfall.

Complex network analysis
We investigate important moisture recycling pathways using two measures from complex network analysis: clustering coefficient associated with Middleman motifs and betweenness centrality.In complex network theory, motifs are defined as significant and recurring patterns of interconnections that occur in the network (Milo et al., 2002).Here, we are interested in a particular pattern of directed triangles: the Middleman motif (Fagiolo, 2007).In our study, a grid cell forms a Middleman motif if it represents an intermediary on an alternative pathway to the direct transport of moisture between two other grid cells (Fig. 3).
The clustering coefficient is a measure from complex network analysis that measures the tendency to form a particular motif (Fagiolo, 2007).Here, it reveals intermediary locations in CMR pathways, as the alternative to the DMR between sources and sinks.To account for moisture fluxes along the 515 network links, we compute the weighted version of the clustering coefficient associated with Middleman motifs ( C) (Fa-giolo, 2007;Zemp et al., 2014) for each grid cell as described in the Appendix B4.1.
A grid cell has a high C if it forms a lot of Middleman 520 motifs and if these motifs contribute largely to relative moisture transport.C is equal to zero if the grid cell forms no Middleman motif at all.It is worth to note that the Middleman motif considers three interconnected grid cells, which corresponds to CMR 525 pathways involving only one re-evaporation cycle.These pathways contribute usually most to moisture transport between two locations.In fact, the amount of moisture transported in a pathway typically decreases with the number of re-evaporation cycles involved in the pathway.This is in 530 agreement with a previous study counting the number of reevaporation cycles using a different methodology (Goessling and Reick, 2013).Other motifs formed by three grid cells linked by moisture recycling have been used to highlight different patterns in moisture transport (e.g., cycle, integration 535 and distribution) (Zemp et al., 2014), but are not analyzed here.

Betweenness centrality (B)
B aims to highlight nodes in the network with central position "to the degree that they stand between others and can 540 therefore facilitate, impede or bias the transmission of messages" in the network (Freeman, 1977, p. 36).Here, we use it to reveal intermediary grid cells where CMR pathways are channeled.
To compute it, we first identify for each pair of grid cells 545 the moisture recycling pathways with the greatest throughput, called "optimal pathways' (see methodology in Appendix B4.2).These pathways can include any number of re-evaporation cycles.As the optimal pathway is usually the direct one (without any re-evaporation cycle), we first had to 550 modify the network such that the optimal pathways involve re-evaporation cycles.To do so, we removed from the network all long-range moisture transport, i.e., occurring over distances larger than 15 geographical degrees.The choice of this threshold does not influence the results qualitatively on a 555 yearly basis (Fig. B3).During the dry season, removing longrange moisture transport affects moisture inflow over the La Plata basin, therefore the results of the B will be interpreted with caution during this season.
Once optimal pathways are identified, we find intermedi- In fact, all three measures reveal important intermediary grid cells in CMR pathways.However, the three measures are based on different concepts and methods.
575 1.While ∆E c /E is calculated by inhibiting reevaporation of moisture from continental origin, B is based on the notion of optimal pathways and C relies on particular motifs formed by three connected grid cells.
2. An implication of ( 1) is that ∆E c /E quantifies the local contribution to CMR, C refers to CMR pathways as alternative to the direct transport of moisture between two locations and B shows locations where CMR pathways are channeled.For these reasons, ∆E c /E, B and C are complementary measures.There are also some similarities between the calculation of the cascading precipitation recycling ratio (ρ casc Ω ) and ∆P c /P , which are described in the appendix B2.
3 Results and discussion 3.1 Comparison of continental and regional moisture 595 recycling ratios with other existing studies The main continental source of precipitation in South America is the Amazon basin, with large heterogeneity in time and space (Figs.1e, 1j, 2e and 2j and Table 3).Around 70 to 80 % of the evapotranspiration in the southern part of the Amazon basin falls as precipitation over the continent during the wet season but only 30 to 40 % during the dry season.As the evapotranspiration in the Amazon basin is high and varies little in space and time (Figs. 1b,1g,2b and 2g), this observation indicates that during the dry season, a high amount of moisture from the southern part of the Amazon basin is advected out of the continent.Using a Lagrangian particle dispersion model, Drumond et al. (2014) also found a maximum contribution of moisture from the Amazon basin to the ocean during this period.
The main sink regions of moisture originating from the continent are the western part of the Amazon basin during the dry season, the south-western part of the basin during the wet season and the La Plata basin especially during the wet season (Figs. 1d,1i,2d and 2di and Table 3).In fact, 615 in the La Plata basin, 42 to 45 % of the precipitation during the wet season and 35 % during the dry season evaporated from the continent.This difference between seasons is explained by a weaker transport of oceanic moisture associated with the subtropical Atlantic high and by an intensification 620 of the South American Low-Level Jet (SALLJ) that transports moisture in the meridional direction during this season (Marengo et al., 2004).The importance of continental moisture recycling in the La Plata basin during the wet season has been emphasized in previous studies (Drumond et al.,625 2008; Martinez et al., 2014).Despite this importance, we find that the ocean remains the main source of moisture over the La Plata basin in agreement with previous studies (Drumond et al., 2008;Arraut and Satyamurty, 2009;Drumond et al., 2014).However, some other studies estimated a higher con-630 tribution of moisture from the continent to precipitation over the La Plata basin (van der Ent et al., 2010;Keys et al., 2012;Martinez et al., 2014).
There are uncertainties in the moisture recycling ratios depending on the quality of the datasets used, the assumptions 635 made in the methods and the boundaries used to define the domain (for example in Brubaker et al., 1993, the Amazon region is represented by a rectangle).Considering these uncertainties, the regional precipitation recycling ratio in the Amazon basin compares well with previous studies using 640 other datasets and methodologies (Table 2).The spatial patterns of continental moisture recycling ratios (Figs. 1d,1i,1e,1j,2d,2i,2e and 2j) are slightly different from those found by (van der Ent et al., 2010, Figs. 3 and 4) due to the differences in the versions of the model (here we use 645 WAM-2layers) and the datasets used.The continental precipitation recycling ratio in the Amazon basin reaching 27 to 30 % during the Southern Hemisphere summer is slightly below estimates of 36.4 % found by Bosilovich and Chern (2006).The maps of DMR ratios (Fig. 8a, and c, e and g) are 650 in good agreement with regional recycling ratio reported in previous studies (Eltahir and Bras, 1994, Figs. 4 and 6 and Burde et al., 2006, Figs. 2 and 8 and Dirmeyer et al., 2009 see http://www.iges.org/wcr/,Moisture Sources by Basin).
We note that our analysis period from 2001-2010 (for the 655 input MOD) includes two major droughts in the Amazon basin (Marengo et al., 2008;Lewis et al., 2011).Because the land-atmosphere coupling on the hydrological cycles increases during drought years (Bagley et al., 2014), this might influence the output of the atmospheric moisture tracking 660 model used in this study.Analyzing these periods separately is ongoing research.

Importance of CMR (cascading moisture recycling)
Continental moisture recycling is of crucial importance for South American precipitation patterns (Figs. 1 and 2).We The share of cascading moisture on total moisture inflow is on average 9 -10 % in the South American continent (Table 3).Regions that are dependent on CMR for local rainfall (Figs.5a, c, e and g) are also dominant sinks of moisture from the continent (Figs. 1d,1i,2d and 2i).
We note that CMR contributes more to the precipitation over the Amazon basin during the dry season (8 -11 % on average, up to 25 % in the western part) compared to the wet season (6 -8 % on average).This is explained by the fact that during the dry season, moisture is mainly transported from the eastern to the western part of the Amazon basin (Figs. 1 and 2).Our results show that during the dry season, this moisture transport involves re-evaporation cycles in the central part of the basin (blue boundaries in Figs.5b and f).
In fact, 15 -23 % of the total evapotranspiration from the Amazon basin is involved in CMR during the dry season.
During the wet season, CMR plays also an important role as 17 -18 % of the total precipitation over the La Plata basin comes from CMR.The intermediary region where 685 re-evaporation cycles are taking place is mainly the southwestern part of the Amazon basin (blue boundaries in Figs.5d and h).In this intermediary region, up to 35 % of the total evapotranspiration is involved in CMR during the wet season.We note that the shape of the intermediary regions varies slightly among the two datasets during the wet season, probably explained by the differences in evapotranspiration patterns (Figs.1g and 2g).
In order to quantify the importance of the intermediary region for rainfall over the La Plata basin, we quantify the share of the moisture inflow in the La Plata basin that has run through re-evaporation cycles in the intermediary regions.This share is 9 % during the wet season and 5 % during the dry season.These estimations represent about half of the share of total moisture inflow over the La Plata basin that comes from CMR during the wet season (Table 3).These results mean that the intermediary regions are important for cascading moisture transported towards the La Plata basin during the wet season.In Sect.3.4, we reveal the direct and cascading sources of precipitation over the La Plata basin and 705 we understand the seasonal variability.
The share of cascading moisture on the total moisture inflow reaches up to 35 -50 % in the eastern side of the central Andes, one of the most vulnerable biodiversity hotspots on Earth (Myers et al., 2000).However, this latter observation should be considered with caution due to the imbalance of the water cycle in this area, which might lead to an over-estimation of the regional recycling process and thus an over-estimation of the importance of cascading moisture recycling.

Complex network analysis
We have shown the importance of CMR for South American moisture transport (Fig. 5).Using the clustering coefficient associated with the Middleman motif ( C), we are able to identify intermediary locations involved in cascad-720 ing pathways as alternative to the direct transport of moisture (Figs.6a, c, e and g).These regions coincide with the intermediary regions identified with a different method (blue boundaries in Fig. 5).These results mean the CMR pathways involving the intermediary regions are not the only pathways 725 of moisture recycled from sources to sinks on the continent, but are complementing the direct transport of moisture over long distances.
The betweenness centrality (B) reveals intermediary regions where CMR pathways are channeled.We note that re-730 gions with high B coincide with regions with high C during the wet season, but not as much during the dry season (Fig. 6).This might be a results of the cutting of long-range links from the network in the calculating of the B, which affects moisture transport towards the subtropical South Amer-735 ica during the dry season.
High values of B are found along a narrow band east of the subtropical Andes (Figs. 6d and h), indicating that CMR pathways are channeled in this region.This observation may be explained by the combined effect of the acceleration of 740 the SALLJ (Vera et al., 2006) and the high precipitation and evapotranspiration during the wet season (Figs. 1 and 2) allowing for an intensive local exchange of moisture between the vegetation and the atmosphere.

Plata basin
We have shown the importance of the Amazon basin as the dominant source of continental moisture and the La Plata basin as a central sink region (see Figs. 1 and 2).In the following, we further investigate the importance of DMR and 750 CMR for the transport of moisture between the two basins (Figs. 7 and 8).
In the La Plata basin, 18 -23 % of the precipitation during the wet season and 21 -25 % during the dry season originated from the Amazon basin with no intervening re-755 evaporation cycles (Table 3).This is in good agreement with the yearly average estimates of 23 % found in Dirmeyer et al. (2009, see http://www.iges.org/wcr/)and 23.9 % found in Martinez et al. (2014).Considering CMR increases the fraction of precipitation that comes from the Amazon basin by 760 6 % during the wet season (Table 3).As mentioned above, this might be explained by the high evapotranspiration and precipitation allowing for an exchange of moisture on the way and by the intensification of the SALLJ during this time of the year (Marengo et al., 2004).This result suggests that 765 the impact of deforestation in the Amazonian forest on rainfall over the La Plata basin might be larger than expected if only direct transport of moisture between the two basins are considered.
The southern part of the Amazon basin is a direct source 770 of precipitation over the La Plata basin (Figs.7a, c, e and g).This finding is in agreement with Martinez et al. (2014) and Keys et al. (2014).However, if CMR is considered, the entire Amazon basin becomes an evaporative source of moisture for the La Plata basin during the wet season (Figs.7d     and h).On average, 16 -23 % of the total evapotranspiration from the Amazon basin during the wet season ends as rainfall over the La Plata basin after at least one re-evaporation cycle (Table 3).This result means that during the wet season, the southern part of the Amazon basin is not only a direct source of moisture for the La Plata basin but also an intermediary region that distributes moisture originating from the entire basin.This finding is in agreement with other measures showing intermediary regions (Sects.3.2 and 3.3).

Possible impact of land-cover change in the intermediary regions
The southern part of the Amazon basin is a key region for moisture transport towards the La Plata basin.It is a source of moisture for precipitation over the La Plata basin all year round.In addition, it is an intermediary region for the indirect transport of moisture (through CMR) originating from the entire Amazon basin during the wet season (Sect.3.4).Land cover change in the southern part of the Amazon basin might weaken continental moisture recycling and might lead to an substantial decrease in the total precipitation locally and downwind.Among the affected regions, important impacts would be observed in particular in the southwestern part of the Amazon basin that has already a high probability to experience a critical transition from forest to savanna (Hirota et al., 2011) and in the La Plata basin that is dependent on incoming rainfall for the agriculture (Rockström et al., 2009;Keys et al., 2012).At the eastern side of the central Andes, the impact of an upwind weakening of CMR might be reduced since precipitation in this region is ensured by orographic lifting (Figueroa and Nobre, 1990).

Conclusions
In this work, we investigated the exchange of moisture between the vegetation and the atmosphere on the way between sources and sinks of continental moisture in South America.We have introduced the concept of "cascading moisture recycling" (CMR) to refer to moisture recycling between two locations on the continent that involve one or more reevaporation cycles along the way.We have proposed measures to quantify the importance of CMR, to track moisture from a given region further backward or forward in space and to identify intermediary regions where re-evaporation cycles are taking place.We have used for the first time a complex network approach to study moisture recycling pathways.
We have tracked moisture evaporating from each grid cell covering the South American continent until it precipitates or leaves the continent using the atmospheric moisture tracking model Water Accounting Model-2layers (WAM-2 layers).In order to reduce the uncertainty associated with the input data, we use two different sets of precipitation and evapotranspiration data from (1) observation-based and (2) merged syn-825 thesis products, together with reanalysis wind speeds and humidity data.We have shown that even if the amount of water transported through CMR pathways is typically smaller than the one transported directly in the atmosphere, the contribution by the ensemble of cascading pathways can't be ne-830 glected.In fact, 9 -10 % of the total precipitation over South America and 17 -18 % of the precipitation over the La Plata basin comes from CMR.The La Plata basin is highly dependent on moisture from the Amazon basin during both seasons, as 18 -23 % of the total precipitation over the La Plata 835 basin during the wet season and 21 -25 % during the dry season comes directly from the Amazon basin.To these direct dependencies, 6 % of the precipitation during the wet season can be added if CMR are considered.
During the dry season, CMR plays an important role for 840 the moisture transport from the eastern to the western part of the Amazon basin.Indeed, 15 -23% of the total evapotranspiration in the Amazon basin is involved in CMR during the dry season.
The south-western part of the Amazon basin is an impor-845 tant direct source of incoming moisture over the La Plata basin all year round.However, during the wet season, it is not only a direct source but also an intermediary region that distributes moisture from the entire Amazon basin into the La Plata basin.Land use change in these regions may weaken 850 moisture recycling processes and may have stronger consequences for rainfed agriculture and natural ecosystems regionally and downwind as previously thought.
In addition, we showed that the eastern flank of the subtropical Andes -located in the pathway of the South Ameri-855 can Low Level Jet -plays an important role in the continental moisture recycling as it channels many cascading pathways.This study offers new methods to improve our understanding of vegetation and atmosphere interactions on the water cycle needed in a context of land use and climate change.-Direct moisture recycling (DMR): moisture recycling with no intervening re-evaporation cycle on the way.
-Intermediary: location where moisture runs through re-evaporation cycle on its way between two locations on the continent (only in the case of CMR).
-Pathway of moisture recycling: set of locations on land involved in moisture recycling.A DMR pathway includes only the starting (evapotranspiration) and the destination (precipitation) locations, while a CMR pathway includes the starting, the destination and the intermediary locations.
-Optimal pathway: the pathway of moisture recycling that contributes most to moisture transport between two locations.It can be a direct or a cascading pathway.
-Direct source: land surface that contributes directly (i.e., through DMR) to rainfall over a given region.
-Cascading source: land surface that contributes indirectly (i.e., through CMR) to rainfall over a given region.

890
-Source: land surface that contributes directly or indirectly to rainfall over given region.
-Direct sink: land surface that is dependent on evapotranspiration coming directly (i.e., through DMR) from a given region for local precipitation.

895
-Cascading sink: land surface that is dependent on evapotranspiration coming indirectly (i.e., through CMR) from a given region for local precipitation.
-Sink: land surface that is dependent on evapotranspiration coming directly or indirectly from a given region 900 for local precipitation.

Appendix B Supplementary description of the method
All grid-cell measures are area-weighted as described in Zemp et al. (2014).

905
B1 CMR (cascading moisture recycling) ratios To calculate the CMR ratios as defined in Sect.2.3.2,we calculate the individual contributions of CMR pathways consisting of k re-evaporation cycles (k ∈ {1, . . ., n}), which add up to the total CMR contribution.We chose a maximum num-910 ber of cycles n = 100, while the contribution of pathways with number of cycles larger than 3 are close to zero.The fraction of precipitation in grid cell j that comes from Ω through CMR involving only one re-evaporation cycle is: where ρ Ωi is the direct precipitation recycling ratio for grid cell i (Sect.2.3.1).Following the same principle as in Eq. ( B1), the fraction of precipitation in j that comes from Ω through CMR involving n re-evaporation cycles is: where ρ is the fraction of precipitation in i that comes from Ω through CMR involving n − 1 re-evaporation cycles.ρ casc Ω is the sum of all individual contributions of the CMR 925 pathways: The fraction of evapotranspiration in grid cell i that falls as precipitation over Ω after only one re-evaporation cycle is: where ε Ω,j is the direct evapotranspiration recycling ratio for grid cell j (Sect.2.3.1).Similarly, the fraction of evapotranspiration in i that falls as precipitation over Ω after n 935 re-evaporation cycles is: where ε is the fraction of evapotranspiration in j that precipitates over Ω after n−1 re-evaporation cycles.The ε casc Ω 940 is the sum of the individual contribution of CMR pathways:  1990-1995 24 B2 Robustness of the CMR (cascading moisture recycling) ratios In order to test the robustness of the cascading precipitation recycling ratios, we have computed the steps explained in B1 with Ω being the ocean.Thus, ρ o is the fraction of precipitation that comes from the ocean without any re-evaporation cycle on the way and ρ o is the fraction of precipitation that comes from the ocean with k re-evaporation cycle(s) on the way (k = 1, ...n).We confirm that: o is equal to 1.This is easy to interpret as all the precipitation in a location must always have been come from the ocean (either directly or after a certain number of re-evaporation cycles).
-The sum ρ represents the fraction of precipitation that comes from the ocean with at least 1 re-evaporation cycle.It is equal to the continental re-960 cycling ratio ρ c (see Sect. 2.3.1 and van der Ent et al. ( 2010)).
-The sum ρ o is the fraction of precipitation that comes from the ocean with at least 2 re-evaporation cycles.It is equal to ∆P/P , introduced as the fraction 965 precipitation that has been evaporated at least twice on the continent (see Sect. 2.4).
We obtained thus the same results using different metrics.We can't test the evaporation recycling ratio the same way because ∆E/E quantifies the fraction of evapotranspi-970 ration that is involved in cascading moisture recycling (i.e., Table 3: Importance of direct moisture recycling (DMR) and cascading moisture recycling (CMR) for the total precipitation (precip.) and evapotranspiration (evap.)averaged for the La Plata basin (LPB), the Amazon basin (AB) and for the South American continent during the wet season (DJFM), the dry season (JJAS) and all year round calculated for the input MOD / LFE (in %). that comes from the continent and precipitates further over the continent) while o would be the fraction of evapotranspiration that runs through at least 2 re-evaporation cycles before precipitating over the ocean.This is also the reason why the two methodologies are needed even if they lead to the same results for the previous mentioned case.

B3 Quantifying CMR (cascading moisture recycling)
To quantify the contribution of CMR in Ω to total moisture in-and outflow, we modify the network such that the oceanic moisture (i.e., that has been last evaporated over the ocean) is only re-evaporated once in Ω.By doing so, we remove CMR in Ω.We then derive the corresponding reduction in total moisture inflow from Ω or outflow towards Ω: where P j←Ω = i∈Ω m ij is the precipitation in j originating from Ω, E i→Ω = j∈Ω m ij is the evapotranspiration in i that precipitates over Ω, P j←Ω,o = i∈Ω m ij←ocean is the precipitation in j originating from the re-evaporation of oceanic moisture in Ω and E i→Ω,o = j∈Ω m ij←ocean is the evapotranspiration of oceanic moisture in i that precipitates over Ω.Thus, ∆P j←Ω is the precipitation in j originating from the re-evaporation of continental moisture in Ω and

995
∆E i→Ω is the re-evaporation of continental moisture in i that precipitates over Ω.If Ω is the entire South American continent (resp.the intermediary region), ∆P j←Ω becomes ∆P c (resp.∆P m ) and ∆E i→Ω becomes ∆E c (resp.∆E m ) as defined in Sect.2.4.

1000
To remove CMR in Ω, we derive for each grid cell the evaporation of moisture from oceanic origin as in Eq. ( 1): where P i←ocean is the precipitation from oceanic ori-1005 gin in i (P j←ocean = P j − P j←continent and P j←continent = i∈continent m ij ) (see Fig. B1).Using the same assumption, we get the moisture transport between each pair of grid cells i and j that results from evaporation of moisture from oceanic origin only: At this stage, m ij←ocean can be interpreted as the evapotranspiration in i that precipitates in j and that has been evaporated from the ocean before that (m ij←ocean < m ij ).

B4 Complex network analysis B4.1 Clustering coefficient associated with Middleman motifs
Mathematically, the clustering coefficient C of the grid cell i is: where t i is the number of Middleman motifs that i forms and T i is the total number of that motif that i could have formed according to its number of incoming and outgoing arrows.
To give more weight to a motif involved in the transport of 1025 a larger amount of moisture, we assign a weight to each motif.In agreement with Fagiolo (2007), the weight of a motif is defined as the geometric mean of the weights of the three involved arrows.The weighted counterpart of Eq. ( B10) is: 1030 with ti the weighted counterpart of t i (i.e., the sum of the weights of the Middleman motifs that is formed by i).
The calculation of the clustering coefficient is derived from the methodology of a previous study (Fagiolo, 2007(Fagiolo, , 1035 Table 1) and has been corrected in order to account for the 0.1 0.3 0.5 0.7 0.9 (j) εc Fig. 2: Same as Fig. 1 for the period 1990-1995 as calculated from LandFluxEval and an average of four observation-based precipitation products (input LFE, see Table 1).irregular sizes of the portion of the Earth's surface covered by the grid cells as explained in Zemp et al. (2014).
We define the matrix P = {p 1/3 ij } obtained by taking the 3 d root of each entry p ij , with p ij being the weight of the arrow originating from i and pointing towards j.Here, in order to avoid a strong correlation between the clustering coefficient and the mean evapotranspiration and precipitation, we chose this weight to be p ij = m 2 ij /(E i P j ).According to Fagiolo (2007), the numerator of Eq. (B11) is derived as the i th element of the main diagonal of a product of matrices ti = (PP T P) ii , where P T is the transpose of P.
The denominator of Eq. (B11) is where k in i is the number of arrows pointing towards i and k out i the number of arrows originating from i: where a ij = 1 if there is an arrow originating from i and pointing towards j and a ij = 0 otherwise.In order to compare the results for the two seasons, we normalize C with the maximum observed value for each network.

B4.2 Optimal pathway
In complex network theory, many centrality measures (e.g.closeness and betweenness) are based on the concept of a shortest path.The shortest path is usually defined as the pathway between nodes that has the minimum cost.In this work, it is defined as the pathway that contributes most to the moisture transport between two grid cells.As this pathway is not necessarily the shortest one in term of geographical dis-1065 tance, we will call it "optimal pathway" to avoid confusion.Let (r 1 , r 2 , . . ., r n ) be the intermediary grid cells in a CMR pathway from grid cell i to grid cell j.The contribution of this pathway is defined as the fraction of precipitation in j that comes from evapotranspiration in i through CMR: An example of pathway contributions is provided in Fig. B2.The contribution of each existing pathway is calculated between any pair of grid cells in the network.The optimal path-1075 way is the path with the maximum contribution.
To find the optimal pathway, we use the method shortest paths in the package iGraph for Python based on an algorithm proposed by Newman (2001).In this method, the cost of a pathway is calculated as the sum of 1080 the weight of its arrows.In order to adapt the method to our purpose, we chose the weight of the arrows as w r l r l+1 = − log mr l r l+1 Pr l+1 . The cost of a pathway from grid cell i to  Because the optimal pathway is defined as the pathway with the minimum cost W , it corresponds to the pathway with the maximum contribution W as defined above.

B4.3 Betweenness centrality
Mathematically, betweenness of the grid cell i is the number 1095 of optimal pathways between any pair of grid cells that pass through i: Fig. 7: Fraction of evapotranspiration that precipitates over the La Plata basin (defined by the purple boundaries) through DMR (ε Pl , a, c, e and g) and CMR (ε casc Pl , b, d, f and h).Considered together, ε Pl and ε casc Pl show source regions of precipitation over the La Plata basin.Results are obtained using the input MOD (upper row) and LFE (lower row) (see Table 1) and are given for the dry season (left) and the wet season (right).with σ jk (i) is the number of optimal pathways between grid cells j and k that pass through the grid cell i.B reaches values between 0 and N −1 2 = (N 2 − 3N + 2)/2 with N the number of grid cells.To calculate it, we used the method betweenness in the package iGraph for Python.This measure is then shifted to a logarithm scale (log10(B + 1)) and normalized by the maximum obtained value.Fig. B3 shows the B for different thresholds in the geographical distance of the links excluded from the network.(h) ρ casc Am Fig. 8: Fraction of precipitation that originates from the Amazon basin (defined by the red boundaries) through DMR (ρ Am , a, c, e and g) and CMR (ρ casc Am , b, d, f and h).Considered together, ρ Am and ρ casc Am show sink regions of evapotranspiration from the La Plata basin.Results are obtained using the input MOD (upper row) and LFE (lower row) (see Table 1) and are given for the dry season (left) and the wet season (right).Fig. B1: Scheme explaining the removal of CMR.Originally, the precipitation in the grid cell i (P i ) is composed by oceanic and continental moisture.The total incoming moisture is evaporated in i (E i ) and some part of it contributes to precipitation in the grid cell j (m ij ) (a).If we forbid the re-evaporation of continental precipitation, only the precipitation in i that has oceanic origin (P i←ocean ) is evaporated in i (E i←ocean ) and can contribute to precipitation in j (m ij←ocean ).By doing so, we remove cascading recycling of continental moisture from the network (b).
500 2.5.1 Clustering coefficient associated with Middleman motifs ( C) 3. In the C, only CMR pathways with one re-evaporation 585 cycle are considered.Using ∆E c /E and B, all number of cycles are possible in the pathways.4. Moisture recycling pathways involving long-range transport are not considered in the calculation of the B.
: the process by which evapotranspiration in a specific location on the continent contributes to precipitation in another location on the con-865 tinent.-Re-evaporationcycle: evapotranspiration of precipitating moisture in the same location -Cascading moisture recycling (CMR): moisture recycling that involves at least one re-evaporation cycle on 870 the way.

Fig. 1 :
Fig.1: WAM-2layers input and output as calculated for the period 2001 -2010 for MODIS and TRMM (input MOD, see Table1): long term seasonal mean of precipitation (a, f), evapotranspiration (b, g), precipitation -evapotranspiration (c, h), continental precipitation recycling ratio ρ c (d, i) and continental evapotranspiration recycling ratio ε c (e, j) indicating respective sinks and sources of continental moisture.Here and in the following figures, the vectors indicate the horizontal moisture flux field (in m 3 of moisture × m −2 × month −1 ) and the hatches represent grid cells where annual mean evapotranspiration exceeds mean annual precipitation.The red boundaries delimit the Amazon basin and the purple lines delimit the La Plata basin.Results are given for the dry season (upper row) and the wet season (lower row).

Fig. 3 :
Fig. 3: Schematic representation of the moisture recycling network.The exchange of moisture from 2 towards 4 uses two alternative pathways: the direct one (m 24 ) and the cascading pathway (m 21 m 14 ).The grid cell 1 is an intermediary on an alternative pathway to the direct transport of moisture between 2 and 4. Thus, grid cell 1 forms a Middleman motif with grid cells 2 and 4.

Fig. 4 :
Fig.4: Schematic representation of the sink and sources regions as quantified by the moisture recycling ratios.In addition to the direct source and sink regions identified using DMR ratios (dark gray), the cascading source and sink regions identified using CMR (light gray) are highlighted.Direct and cascading sink regions of evapotranspiration (evap.)from the Amazon basin (AB) (a) and direct and cascading source regions of precipitation (precip.)over the La Plata basin (LPB) (b).

Fig. 6 :
Fig. 6: Results of complex network analysis.Clustering coefficient C associated with the motif Middleman (a, c, e, g) and betweenness centrality B (b, d, f, h).While high values of C indicate intermediary locations where CMR allows for alternative pathways to the direct transport of moisture, high values of B indicate regions where pathways of CMR are channeled.Results are obtained using the input MOD (upper row) and LFE (lower row) (see Table1) and are given for the dry season (left) and the wet season (right).
∆E c /E is the fraction of total evapotranspiration that is a re-evaporation of moisture originating from the continent and that further precipitates over the continent, i.e., that lies within CMR pathways.∆E c /E quantifies the local contribution to CMR. High values of ∆E c /E indicate intermediary regions.Regions that have a larger ∆E c /E than the 80 percentile (calculated for all seasonal values over the continent) are called "intermediary" regions in the following.
c /P quantifies the importance of CMR for local rain-475 fall.
A grid cell has a high B if many optimal pathways pass through it, i.e., moisture runs often through re-evaporation cycle in the grid cell.It has a B equal to 0 if none of these pathways pass through it, i.e., moisture never runs through 565 re-evaporation cycle in the grid cell.

Table 1 :
Input datasets used for building moisture recycling networks.The first year of the period is omitted from the results because of model spin-up.

Table 2 :
Overview of regional precipitation recycling ratio in the Amazon basin as found in many studies.Abbreviations: the European Centre for Medium-Range Weather Forecasts (ECMW); Geophysical Fluid Dynamics Laboratory Precipitation (GFDL); Climate Prediction Center Merged Analysis of Precipitation (CMAP); Initinal conditions (IC); October-November-December (OND); Data Assimilation Office (DAO); Integral Moisture Balance (IMB) model; NCEP -Department of Energy (DOE); World Monthly Surface Station Climatology distributed by the National Center for Atmospheric Research (NCAR).
Fig.5: Fraction of total precipitation originating from CMR (∆P c /P ) (a, c, e, g) and fraction of total evapotranspiration that lies within CMR pathways (∆E c /E) (b, d, f, h).While high values of ∆P c /P indicate regions that are dependent on CMR for local rainfall, high values of ∆E c /E indicate regions that contribute to CMR.The blue boundaries define the regions that have ∆E c /E > 80 percentile (calculated for all seasonal values over the continent) and that are called "intermediary" regions.Results are obtained using the input MOD (upper row) and LFE (lower row) (see Table1) and are given for the dry season (left) and the wet season (right).