Cascading Moisture Recycling Increases

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icsinPpr|Dsuso ae icsinPpr|Dsuso ae | Paper Discussion | Paper Discussion | Paper Discussion | Paper Discussion Atmos. Chem. Phys. Discuss., 14, 17479–17526, 2014 www.atmos-chem-phys-discuss.net/14/17479/2014/ doi:10.5194/acpd-14-17479-2014 ACPD © Author(s) 2014. CC Attribution 3.0 License. 14, 17479–17526, 2014

This discussion paper is/has been under review for the journal Atmospheric Chemistry Cascading moisture and Physics (ACP). Please refer to the corresponding ﬁnal paper in ACP if available. recycling On the importance of cascading moisture D. C. Zemp et al. recycling in South America Title Page

Abstract Introduction D. C. Zemp1,2, C.-F. Schleussner3, H. M. J. Barbosa4, R. J. Van der Ent5, 1,6 1 7 1 J. F. Donges , J. Heinke , G. Sampaio , and A. Rammig Conclusions References

1Potsdam Institute for Climate Impact Research (PIK), Telegraphenberg A 31, 14473 Tables Figures Potsdam, Germany 2 Department of Geography, Humboldt Universität zu Berlin, Berlin, Germany J I 3Climate Analytics, Berlin, Germany 4Instituto de Física, Universidade de São Paulo, São Paulo, S.P., Brazil J I 5 Department of Water Management, Faculty of Civil Engineering and Geosciences, Delft Back Close University of Technology, Delft, the Netherlands 6Stockholm Resilience Centre, Stockholm University, Kräftriket 2B, 114 19 Stockholm, Sweden Full Screen / Esc 7Center for Earth System Science (CCST), INPE, Cachoeira Paulista, S.P., Brazil Printer-friendly Version Received: 12 May 2014 – Accepted: 8 June 2014 – Published: 30 June 2014 Interactive Discussion Correspondence to: D. C. Zemp ([email protected]) Published by Copernicus Publications on behalf of the European Geosciences Union.

17479 icsinPpr|Dsuso ae icsinPpr|Dsuso ae | Paper Discussion | Paper Discussion | Paper Discussion | Paper Discussion Abstract ACPD Continental moisture recycling is a crucial process of the South American climate system. Evapotranspiration from the Amazon river basin contributes to precipitation re- 14, 17479–17526, 2014 gionally and in the La Plata river basin. Here we present an in-depth analysis of South 5 American moisture recycling. We quantify the importance of “cascading moisture re- Cascading moisture cycling”, which describes the exchange of moisture between the vegetation and the recycling atmosphere through precipitation and re-evaporation cycles on its way between two locations on the continent. We use the Water Accounting Model 2-layers (WAM-2layers) D. C. Zemp et al. forced by precipitation from TRMM and evapotranspiration from MODIS for the period 10 2001 until 2010 to construct moisture recycling networks. These networks describe the direction and amount of moisture transported from its source (evapotranspiration) to Title Page its destination (precipitation) in South America. Model-based calculations of continen- Abstract Introduction tal and regional recycling ratios in the Amazon basin compare well with other existing studies using diﬀerent datasets and methodologies. Our results show that cascading Conclusions References 15 moisture recycling contributes about 10 % to the total precipitation over South America Tables Figures and 17 % over the La Plata basin. Considering cascading moisture recycling increases

the total dependency of the La Plata basin on moisture from the Amazon basin by J I about 25 % from 23 to 29 % during the wet season. Using tools from complex network analysis, we reveal the importance of the south-western part of the Amazon basin as J I 20 a key intermediary region for continental moisture transport in South America during Back Close the wet season. Our results suggest that land use change in this region might have a stronger impact on downwind rainfed agriculture and ecosystem stability than previ- Full Screen / Esc ously thought. Printer-friendly Version

Interactive Discussion 1 Introduction

25 Continental moisture recycling, the process by which evapotranspiration from the continent returns as precipitation to the continent (Brubaker et al., 1993; Eltahir and 17480 icsinPpr|Dsuso ae icsinPpr|Dsuso ae | Paper Discussion | Paper Discussion | Paper Discussion | Paper Discussion Bras, 1994; van der Ent et al., 2010) is particularly important for the South American hydrological cycle. In the Amazon river basin, between 25 and 35 % of the moisture ACPD is regionally recycled (Eltahir and Bras, 1994; Trenberth, 1999; Bosilovich and Chern, 14, 17479–17526, 2014 2006; Burde et al., 2006; Dirmeyer et al., 2009). The moisture from the Amazon basin 5 is also exported out of the basin, transported via the South American Low Level Jet along the Andes and contributes to precipitation over the La Plata river basin particu- Cascading moisture larly during the wet season (Marengo, 2005; Drumond et al., 2008, 2014; Arraut and recycling Satyamurty, 2009; Dirmeyer et al., 2009; van der Ent et al., 2010; Arraut et al., 2012; Martinez et al., 2014). D. C. Zemp et al. 10 Land-use change – in particular deforestation in the Amazon basin – impacts the evapotranspiration rate and aﬀects the water cycle (see review in Marengo, 2006). Title Page A resulting reduction in regional moisture supply may have important consequences for the ecosystem stability in the Amazon rainforests (Oyama and Nobre, 2003; Cox Abstract Introduction et al., 2004; Betts et al., 2004; Hirota et al., 2011; Knox et al., 2011; Spracklen et al., Conclusions References 15 2012). Downwind, e.g., in the La Plata basin, rainfall reduction may aﬀect rainfed agriculture (Rockström et al., 2009; Keys et al., 2012). Even if regional impact of changes Tables Figures in precipitation patterns from deforestation has been intensively studied using simula- tions from atmospheric general circulation models with deforestation scenarios (Lean J I and Warrilow, 1989; Shukla et al., 1990; Nobre et al., 1991, 2009; Werth and Avissar, J I 20 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 Back Close and the location of the most impacted regions are still uncertain. Therefore, further Full Screen / Esc advancements in our understanding of the continental moisture recycling in the South American continent are needed. Printer-friendly Version 25 To identify sources and sinks of moisture and to quantify regional and continental moisture recycling in South America, several methods have been used including iso- Interactive Discussion topes (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), quasi-isentropic back-trajectory method (Dirmeyer et al., 2009; Bagley

17481 icsinPpr|Dsuso ae icsinPpr|Dsuso ae | Paper Discussion | Paper Discussion | Paper Discussion | Paper Discussion et al., 2014) and tagged water experiments with a general circulation model (GCM) (Bosilovich and Chern, 2006) or a posteriory with reanalysis data (Sudradjat et al., ACPD 2002; van der Ent et al., 2010; Keys et al., 2012) (see a review of the methods in 14, 17479–17526, 2014 van der Ent et al., 2013; Burde and Zangvil, 2001). In most of existing studies using 5 tagged water experiments, moisture evaporating from a given region is tracked forward in time from the evapotranspiration until it returns to the land surface as precipita- Cascading moisture tion. However, precipitating water can be re-evapotranspirated in the same location recycling (re-evaporation cycle) and can be transported to a downwind location where it contributes to precipitation. Such exchanges of moisture between the vegetation and the D. C. Zemp et al. 10 atmosphere through re-evaporation cycles might play a crucial role for the transport of moisture in the Tropics (Spracklen et al., 2012). Adding diﬀerent types of tracers Title Page within a GCM, Numaguti (1999) found that moisture runs on average through more than two re-evaporation cycles between evaporation from the ocean and precipitation Abstract Introduction in northern Eurasia. In this study we focus for the ﬁrst time on the following questions: Conclusions References 15 1. what is the importance of cascading moisture recycling in South America? Tables Figures 2. Which are the important intermediary regions for cascading moisture recycling? 3. Which are the key regions where the pathways of cascading moisture recycling J I

are channeled? J I

We call “cascading moisture recycling” the process by which evapotranspiration from Back Close 20 a speciﬁc location on land runs through one or more re-evaporation cycles before it precipitates in another one. On the other hand, “direct moisture recycling” refers to the Full Screen / Esc process by which evapotranspiration is directly transported (without any re-evaporation cycle) from one location on land to another, where it precipitates. We call “intermediary” Printer-friendly Version

the location where re-evaporation cycle is occurring. We define a “pathway of moisture Interactive Discussion 25 recycling” as the set of locations including the starting and the destination locations, as well as the intermediaries. We perform a tagged water experiment a posteriori with precipitation, evapotranspiration, wind and humidity datasets from reanalysis and satellite products for South 17482 icsinPpr|Dsuso ae icsinPpr|Dsuso ae | Paper Discussion | Paper Discussion | Paper Discussion | Paper Discussion America using the numerical atmospheric moisture tracking model WAM-2layers (Wa- ter Accounting Model-2layers) (van der Ent et al., 2014). ACPD We propose a novel framework to quantify the importance of cascading moisture 14, 17479–17526, 2014 recycling for the regional climate in South America, and in particular in the Amazon 5 basin and the La Plata basin. In addition, we use tools from complex network theory to improve our understanding of moisture recycling pathways in South America. The po- Cascading moisture tential of the complex network approach has been recently shown in climate science. It recycling has been used to detect large-scale related climate anomalies (teleconnections) (Tso- nis et al., 2008; Donges et al., 2009a, b) and to reveal important regions for propagation D. C. Zemp et al. 10 of extreme events (Malik et al., 2012; Boers et al., 2013). In previous studies, links in the network were usually built according to the strength of the statistically relationships Title Page between time series in different locations. In our study, we apply complex network approach for the first time to a network in which the links represent water fluxes. Abstract Introduction In Sect. 2.1 we describe the tagged water experiment using the WAM-2layers and we Conclusions References 15 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 measures in Sects. 2.3 Tables Figures and 2.4 and we present the complex network measures in Sect. 2.5. After comparing the continental and regional recycling ratios with other existing studies in Sect. 3.1, we J I present and discuss new results on the importance of cascading moisture recycling in J I 20 Sect. 3.2 and on complex network analysis in Sect. 3.3. Finally, we present an in-depth analysis of the moisture recycling between the Amazon basin and the La Plata basin Back Close in Sect. 3.4. Full Screen / Esc

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Interactive Discussion

17483 icsinPpr|Dsuso ae icsinPpr|Dsuso ae | Paper Discussion | Paper Discussion | Paper Discussion | Paper Discussion 2 Methods ACPD 2.1 Building moisture recycling networks 14, 17479–17526, 2014 2.1.1 Description of the moisture tracking in WAM-2layers Cascading moisture In this study we make use of the Eulerian atmospheric moisture tracking model WAM- recycling 5 2layers V2.3.01 (van der Ent et al., 2014). The actual tracking in WAM-2layers is performed a posteriori with reanalysis and satellite datasets (see input data in Sect. 2.1.2). D. C. Zemp et al. Evapotranspiration from a certain region of interest is “tagged” and subsequently tracked in the atmosphere by applying water balance principles to each grid cell, consisting of a well-mixed upper and lower part. The two-layer approach is simplified com- Title Page 10 pared to full-3-D tracking, but was shown to perform comparably well (van der Ent et al., 2013). Abstract Introduction WAM-2layers provides the basis for the construction of moisture recycling networks Conclusions References analyzed in the following. To this extent, we performed separate forward tracking runs of evapotranspiration for each continental grid cell in the South American domain (Fig. 4) Tables Figures 15 for the years 2000–2010. The tagged moisture is assumed to be gone when it leaves the domain. We omitted the year 2000 from the results because of model spin-up. The J I output for the years 2001–2010 are aggregated first to monthly, then to seasonally J I average imports and exports between all land grid cells. These seasonal averages Back Close are used to build two seasonal moisture recycling networks which are assumed to be 20 static for the whole season. This implies that in the proposed analysis, for each season Full Screen / Esc moisture is tracked forward and backward in space but not in time. Printer-friendly Version 2.1.2 Input of WAM-2layers Interactive Discussion The input for WAM-2layers are 3 hourly precipitation estimates from the Tropical Rain- fall Measuring Mission (TRMM) based on the algorithm 3B-42 (version 7) (Huffman 25 et al., 2007), 8 days evapotranspiration estimates from Moderate Resolution Imaging

17484 icsinPpr|Dsuso ae icsinPpr|Dsuso ae | Paper Discussion | Paper Discussion | Paper Discussion | Paper Discussion Spectroradiometer (MODIS) based on the MOD16 ET algorithm (Mu et al., 2011) as well as 6 hourly specific humidity and wind speed in three dimensions from the ERA- ACPD Interim reanalysis product (Dee et al., 2011). We downscaled the MODIS evapotran- 14, 17479–17526, 2014 spiration to a 3 hourly resolution based on ERA-Interim, as WAM-2layers needs finer ◦ 5 temporal resolution in the input data. All data is upscaled to a regular grid of 1.5 longitude/latitude and covers the South American continent until 50◦ S, which is the Cascading moisture southernmost latitude covered by TRMM product. In addition, all data is downscaled to recycling 0.5 h as requested by the numerical scheme of WAM-2layers. Humidity estimation has been improved in the ERA-Interim product in comparison D. C. Zemp et al. 10 with others reanalysis products (Dee and Uppala, 2008). Precipitation dataset from TRMM are considered reliable over South America and in particular in the Amazonian Title Page region where others products perform poorly due to the lack of ground based mea- surements (Franchito et al., 2009; Rozante et al., 2010). TRMM precipitation dataset Abstract Introduction are shown to represent high frequency variability sufficiently well (Kim and Alexander, Conclusions References 15 2013). However, it is systematically biased during the dry season in the northeastern coast of Brazil, where precipitation is underestimated (Franchito et al., 2009) and at Tables Figures the junction of Argentina, Paraguay and Brazil, where it is overestimated (Rozante and Cavalcanti, 2008). Evapotranspiration is estimated using a recently improved algorithm J I (Mu et al., 2011) based on the Penman–Monteith equation (Monteith et al., 1965) and J I 20 forced by satellite data from MODIS and meteorological reanalysis data. The quality of the evapotranspiration dataset depends on the quality of the input data and the Back Close parametrization of the algorithm. The evapotranspiration dataset has been validated Full Screen / Esc with 10 eddy flux towers located in the Amazonian region under various land cover types (Loarie et al., 2011; Ruhoff, 2011). Printer-friendly Version 25 The long term seasonal average of evapotranspiration and precipitation as well as moisture flux divergence (evapotranspiration – precipitation) are shown in Fig. 4. The Interactive Discussion 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

17485 icsinPpr|Dsuso ae icsinPpr|Dsuso ae | Paper Discussion | Paper Discussion | Paper Discussion | Paper Discussion System (SAMS) (Liebman et al., 1999; Grimm et al., 2004; Arraut and Satyamurty, 2009). The evapotranspiration is high in the Amazon basin and varies little in time and ACPD space. It exceeds the total precipitation in the southern part of the Amazon basin during 14, 17479–17526, 2014 the dry season, indicating that this region is a net source of moisture for the atmosphere 5 (Fig. 4c). 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 Cascading moisture during the dry season due to the deep root system which enables the pumping of recycling the water from the deeper water table (Nepstad et al., 1994; Miguez-Macho and Fan, 2012). D. C. Zemp et al. 10 We ﬁnd that, averaged over the full time period, evapotranspiration exceeds precipitation in northeastern Brazil, in the Atacama Desert and along the Andes. Possible Title Page explanations for the imbalance in these arid to semi-arid regions are irrigation or bi- ases in the input data as mentioned above. As this might lead to a bias in moisture Abstract Introduction recycling ratios due to an overestimation of the contribution of evapotranspiration to Conclusions References 15 local precipitation, we will exclude these grid cells from our analysis. Tables Figures 2.1.3 Output of WAM-2layers as a complex network

J I The output of WAM-2layers is a matrix M = {mij }i,j∈N with N the number of grid cells in the continent (N = 681). The non-diagonal element mij is the amount of evapotranspi- J I i j m ration in grid cell which precipitates in grid cell and the diagonal element ii is the Back Close 20 amount of evapotranspiration which precipitates in the same grid cell (locally recycled moisture). The output of WAM-2layers can transformed into a directed and weighted Full Screen / Esc complex network with self-interactions, where nodes of the network represent grid cells and links between nodes represent the direction and amount of moisture transported Printer-friendly Version

between them (Fig. 1). Interactive Discussion

17486 icsinPpr|Dsuso ae icsinPpr|Dsuso ae | Paper Discussion | Paper Discussion | Paper Discussion | Paper Discussion 2.2 Basic assumptions ACPD In order to track moisture forward or backward from a given region Ω which can be of any shape and scale (grid cell, basin, continent), we assume that the moisture com- 14, 17479–17526, 2014 position within the surface reservoir and the atmosphere for each grid cell remains 5 the same. This implies that, in each grid cell, the tagged fraction of precipitation is lin- Cascading moisture early proportional to the tagged fraction of evapotranspiration and the tagged fraction recycling of transported moisture: D. C. Zemp et al. P E m Ω = Ω = Ω , (1) P E m Title Page 10 where E is the total evapotranspiration, P is the total precipitation, m is the transported Abstract Introduction moisture towards or from another grid cell, PΩ is the tagged fraction of precipitation, E is the tagged fraction of evapotranspiration and m is the tagged fraction of trans- Ω Ω Conclusions References ported moisture towards or from another grid cell. We call “tagged fraction” the share of the moisture originating from Ω in the case of a backward tracking and the share of Tables Figures 15 moisture precipitating over Ω in the case of a forward tracking. This assumption is valid under two conditions: (1), evapotranspiration follows directly J I after the precipitation event or (2), the fraction of tagged moisture in the surface reser- J I voir 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 inter- Back Close 20 ception and fast transpiration which are important components of the total evapotran- Full Screen / Esc spiration, particularly in warm climates and for shallow rooted plants (Savenije, 2004). However, in seasonal forests with deep rooted trees, the moisture which is evaporated Printer-friendly Version during the dry season can be hold back for one or several months (Savenije, 2004). The second condition is fulfilled if the soil water at the beginning has the same composition Interactive Discussion 25 (in term of tagged fraction) as the atmospheric moisture at the end of the season.

17487 icsinPpr|Dsuso ae icsinPpr|Dsuso ae | Paper Discussion | Paper Discussion | Paper Discussion | Paper Discussion 2.3 Moisture recycling ratio ACPD In this section, we deﬁne measures to track moisture from a given region forward or backward in space. In the case of a forward tracking, the measures indicate the desti- 14, 17479–17526, 2014 nation (precipitative sink) of evapotranspiration from the region. In the case of a back- 5 ward tracking, they indicate the origin (evaporative source) of precipitation over the Cascading moisture region. We ﬁrst consider direct moisture recycling only (Sect. 2.3.1). We then track recycling moisture further forward or backward in space through cascading moisture recycling (Sect. 2.3.2). Considered together, the direct and cascading moisture recycling ratios D. C. Zemp et al. provide a full picture of the sources and sinks of moisture from a region of interest.

10 2.3.1 Direct moisture recycling ratios Title Page

We deﬁne the direct precipitation recycling ratio as the fraction of precipitation in each Abstract Introduction grid cell i that comes directly from evapotranspiration from Ω: Conclusions References

Pi←Ω Tables Figures ρΩ,i = , (2) Pi J I 15 where Pi←Ω is the amount of precipitation in i that is originating from evapotranspiration J I from Ω through direct moisture recycling and Pi is the total precipitation in i (see also Appendix A1). ρΩ quantiﬁes the dependency on direct moisture recycling from Ω for Back Close local rainfall. High values indicate locations which receive moisture (direct precipitative Full Screen / Esc sink) from Ω. We note that ρΩ averaged over all grid cells in Ω gives the regional 20 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, 2011). Printer-friendly Version We also deﬁne the direct evapotranspiration recycling ratio as the fraction of evapo- Interactive Discussion transpiration in each grid cell i that contributes directly to precipitation over Ω:

Ei→Ω εΩ,i = , (3) 25 Ei 17488 icsinPpr|Dsuso ae icsinPpr|Dsuso ae | Paper Discussion | Paper Discussion | Paper Discussion | Paper Discussion where Ei→Ω is the amount of evapotranspiration in i that contributes to precipitation over Ω through direct moisture recycling and Ei the total evapotranspiration in i (see ACPD also Appendix A1). ε quantifies the local contribution to precipitation over Ω through Ω 14, 17479–17526, 2014 direct moisture recycling. High values indicate locations which distribute moisture (di- 5 rect evaporative source) over Ω. If Ω is the entire South American continent, εΩ becomes the continental evapotran- Cascading moisture spiration recycling ratio (εc) and ρΩ the continental precipitation recycling ratios (ρc) recycling as defined in van der Ent et al. (2010). Considered together, εc and ρc indicate respectively sources and sinks of continental moisture. In this study we neglect possible D. C. Zemp et al. 10 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). Title Page To study the direct moisture recycling between the Amazon basin and the La Plata basin (defined by the red boundaries in Fig. 7), we use ρΩ with Ω being all grid cells Abstract Introduction covering the Amazon basin (ρAm) and εΩ with Ω being all grid cells covering the La Conclusions References 15 Plata basin (εPl). While ρAm is useful to track moisture from the Amazon basin as a whole, εPl provides information regarding the spatial heterogeneity of the contribution Tables Figures inside the Amazon basin. The direct recycling ratios underestimate the strength of the relationship, in term of J I moisture recycling, between two specific locations. In fact, moisture can be exchanged J I 20 not only through direct moisture recycling, but also through cascading moisture recycling. Back Close

2.3.2 Cascading moisture recycling ratios Full Screen / Esc

We define the cascading precipitation recycling ratio as the fraction of precipitation in Printer-friendly Version each grid cell i that is originating from evapotranspiration from through cascading Ω Interactive Discussion 25 moisture recycling: P casc ρcasc i←Ω , (4) Ω,i = Pi 17489 casc | Paper Discussion | Paper Discussion | Paper Discussion | Paper Discussion where Pi←Ω is the amount of precipitation in i that is originating from evapotranspiration from through cascading moisture recycling. ρcasc quantifies the dependency Ω Ω ACPD on cascading moisture recycling from Ω for local rainfall. High values indicate the fi- 14, 17479–17526, 2014 nal destination of moisture from Ω after one ore more re-evaporation cycles (indirect 5 precipitative sink). We also define the cascading evapotranspiration recycling ratio as the fraction of Cascading moisture evapotranspiration in each grid cell i which contributes to precipitation over Ω through recycling cascading moisture recycling as: D. C. Zemp et al. E casc εcasc = i→Ω , (5) Ω,i E 10 i Title Page casc where Ei→Ω is the amount of evapotranspiration in i that contributes to precipitation Abstract Introduction over through cascading moisture recycling. εcasc quantifies the local contribution to Ω Ω precipitation over Ω through cascading moisture recycling. High values indicate loca- Conclusions References

tions where moisture initially originated (indirect evaporative source) before it is dis- Tables Figures 15 tributed over Ω. The moisture inﬂow (resp. outﬂow) that crosses the border of Ω may be counted J I several times as it is involved in several pathways of cascading moisture recycling. To avoid this, we only track moisture that crosses the border of Ω. This implies that we J I

consider re-evaporation cycles outside Ω only (Fig. 2, see also Appendix A2). Back Close 20 To study the cascading moisture recycling between the Amazon basin and the La Plata basin, we use ρcasc with being all grid cells covering the Amazon basin (ρcasc) Full Screen / Esc Ω Ω Am and εcasc with being all grid cells covering the La Plata basin (εcasc). While ρcasc con- Ω Ω Pl Am siders cascading recycling of moisture originating from the Amazon basin (see Fig. 2a), Printer-friendly Version εcasc Pl provides information regarding the importance of cascading recycling of moisture Interactive Discussion 25 that has ﬁnal destination the La Plata basin (see Fig. 2b). Considered together, the direct and cascading recycling ratios provide a full picture of the origin and destination of moisture from a given region. High values of ρAm and ρcasc Am indicate together the precipitative sink region of moisture from the Amazon basin 17490 icsinPpr|Dsuso ae icsinPpr|Dsuso ae | Paper Discussion | Paper Discussion | Paper Discussion | Paper Discussion ρ ρcasc and high values of Am and Am highlight evaporative source regions of precipitation over the La Plata basin. ACPD

2.4 Quantifying cascading moisture recycling 14, 17479–17526, 2014

In this section, we are interested in the importance of cascading moisture recycling Cascading moisture 5 for the total moisture inflow (precipitation) and outflow (evapotranspiration). To quantify recycling this, we forbid re-evaporation of moisture originating from the continent and we estimate the resulting reduction in total moisture inflow (∆Pc) and outflow (∆Ec) (see Appendix D. C. Zemp et al. B). ∆Pc/P is the fraction of precipitation that comes from cascading moisture recycling on the continent, i.e., that has been evaporated at least twice on the continent. It quan- Title Page 10 tifies the dependency on cascading moisture recycling for local rainfall. ∆Ec/E is the fraction of total evapotranspiration that is involved in cascading moisture recycling on Abstract Introduction the continent, i.e., that comes from the continent and that further precipitates over the continent. It quantifies the contribution of a specific location to cascading moisture re- Conclusions References

cycling. Regions which have a larger ∆Ec/E than the 80 percentile (corresponding to Tables Figures 15 0.27 during the wet season and 0.17 during the dry season) are called "intermediary regions". J I In addition, we are interested in the importance of cascading moisture recycling in the intermediary regions for the total moisture in- and outﬂow. We use the same approach J I

as above. We forbid re-evaporation in the intermediary region of moisture originat- Back Close 20 ing from the continent and we estimate the resulting reduction in total moisture inﬂow Full Screen / Esc (∆Pm) (see Appendix B). ∆Pm/P is the fraction of total moisture inﬂow that comes from cascading moisture recycling in the intermediary region. It can be seen as the fraction of precipitation that comes from the continent and that has been re-evaporated in the Printer-friendly Version

intermediary region. It quantiﬁes the dependency on cascading moisture recycling in Interactive Discussion 25 the intermediary region for local rainfall.

17491 icsinPpr|Dsuso ae icsinPpr|Dsuso ae | Paper Discussion | Paper Discussion | Paper Discussion | Paper Discussion 2.5 Complex network analysis ACPD We investigate important moisture recycling pathways using two measures from complex network analysis: clustering coeﬃcient associated with Middleman motifs and be- 14, 17479–17526, 2014 tweenness centrality. Cascading moisture 5 2.5.1 Clustering coeﬃcient associated with Middleman motifs recycling

In complex network theory, motifs are defined as significant and recurring patterns of D. C. Zemp et al. 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 is an intermediary on an alternative Title Page 10 pathway to the direct transport of moisture between two other grid cells (Fig. 3). The clustering coefficient is a measure from complex network analysis which mea- Abstract Introduction sures the tendency to form a particular motif (Fagiolo, 2007). Here, it reveals intermedi- Conclusions References ary locations in cascading moisture recycling pathways, as the alternative to the direct recycling of moisture between sources and sinks. We compute the weighted version of Tables Figures 15 the clustering coefficient associated with Middleman motifs (C˜ )(Fagiolo, 2007; Zemp et al., 2014) for each grid cell as described in the Appendix C1. A grid cell has a high J I ˜ C if it forms a lot of Middleman motifs and if these motifs contribute largely to relative J I moisture transport. C˜ is equal to zero if the grid cell forms no Middleman motif at all. Back Close It is worth to note that the Middleman motif considers three interconnected grid cells 20 which corresponds to cascading moisture recycling pathways involving only one re- Full Screen / Esc evaporation cycle. These pathways contribute usually most to moisture transport between two locations. In fact, the amount of moisture transported in a pathway typically Printer-friendly Version decreases with the number of re-evaporation cycles involved in the pathway. Other mo- Interactive Discussion tifs formed by three or more grid cells linked by moisture recycling exist (Zemp et al., 25 2014), but are not analyzed here.

17492 icsinPpr|Dsuso ae icsinPpr|Dsuso ae | Paper Discussion | Paper Discussion | Paper Discussion | Paper Discussion 2.5.2 Betweenness centrality ACPD The betweenness centrality (B) aims to highlight nodes in the network with central position “to the degree that they stand between others and can therefore facilitate, 14, 17479–17526, 2014 impede or bias the transmission of messages” in the network (Freeman, 1977, p. 36). 5 Here, we use it to reveal intermediary grid cells where cascading moisture recycling Cascading moisture pathways are channeled. recycling To compute it, we first identify for each pair of grid cells the moisture recycling pathways with the greatest throughput, called “optimal pathways”. These pathways can D. C. Zemp et al. include any number of re-evaporation cycles. As the optimal pathway is usually the 10 direct one (without any re-evaporation cycle), we first had to modify the network such that the optimal pathways involve cascading moisture recycling. To do so, we removed Title Page from the network all long-range moisture transport, i.e, occurring over distances larger Abstract Introduction than 15 geographical degrees. The choice of this threshold does not influence the results qualitatively. Once optimal pathways are identified, we find intermediary grid cells Conclusions References 15 that they have in common (see Appendix C2). A grid cell has a high B if many optimal Tables Figures pathways pass through it, i.e., moisture often cascades in the grid cell, and has a B

equal to 0 if none of these pathways pass through it, i.e., moisture never cascades in J I the grid cell. J I

2.5.3 Similarities and diﬀerences between the betweenness centrality and the Back Close 20 Middleman motif Full Screen / Esc We expect similar spatial patterns in the results of the B (Sect. 2.5.2) and the C˜ (Sect. 2.5.1). In fact, both measures reveal important intermediary grid cells in cascad- Printer-friendly Version ing moisture recycling pathways. However, these two measures are based on diﬀerent Interactive Discussion concepts and methods.

25 1. While the B is based on the optimal pathways, the C˜ relies on particular motifs formed by three connected grid cells.

17493 icsinPpr|Dsuso ae icsinPpr|Dsuso ae | Paper Discussion | Paper Discussion | Paper Discussion | Paper Discussion 2. An implication of (1) is that the C˜ refers to cascading moisture recycling pathways as alternative to the direct transport of moisture between two locations, while the ACPD B shows locations where cascading moisture recycling pathways are channeled. 14, 17479–17526, 2014 3. In the C˜ , only cascading moisture recycling pathways with one re-evaporation 5 cycle are considered. In the B, all number of cycles are possible in the pathways. Cascading moisture 4. Moisture recycling pathways involving long-range transport are not considered in recycling the calculation of the B. D. C. Zemp et al. For these reasons, the B and the C˜ are complementary measures.

Title Page 3 Results and discussion Abstract Introduction

10 3.1 Comparison of continental and regional moisture recycling ratios with other Conclusions References existing studies Tables Figures The main continental source of precipitation in South America is the Amazon basin, with large heterogeneity in time and space (Fig. 4e and j and Table 2). The southern J I part of the Amazon basin contributes 80 % to continental precipitation during the wet J I 15 season but only 40 % during the dry season. As the evapotranspiration in the Amazon basin is high and varies little in space and time (Fig. 4b and g), this observation indi- Back Close

cates that during the dry season, a high amount of moisture from the southern part of Full Screen / Esc the Amazon basin is advected out of the continent. Using a Lagrangian particle disper-

sion model, Drumond et al. (2014) also found a maximum contribution of moisture from Printer-friendly Version 20 the Amazon basin to the ocean during this period. The main sink regions of moisture originating from the continent are the western part Interactive Discussion 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 (Fig. 4d and i and Table 2). In fact, in the La Plata basin, 42 % of the precipitation during the wet 17494 icsinPpr|Dsuso ae icsinPpr|Dsuso ae | Paper Discussion | Paper Discussion | Paper Discussion | Paper Discussion 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 ACPD with the subtropical Atlantic high and by an intensification of the South American Low- 14, 17479–17526, 2014 Level Jet (SALLJ) which transports moisture in the meridional direction during this 5 season (Marengo et al., 2004). The importance of continental moisture recycling in the La Plata basin during the wet season has been emphasized in Drumond et al. (2008); Cascading moisture Martinez et al. (2014). Despite this importance, we find that the ocean remains the main recycling source of moisture in the La Plata basin in agreement with previous studies (Drumond et al., 2008; Arraut and Satyamurty, 2009; Drumond et al., 2014). However, some other D. C. Zemp et al. 10 studies estimated a higher contribution 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., Title Page 2014). There are uncertainties in the moisture recycling ratios depending on the quality of Abstract Introduction the datasets used, the assumptions made in the methods and the boundaries used Conclusions References 15 to define the domain (for example in Brubaker et al., 1993, the Amazon region is represented by a rectangle). Considering these uncertainties, the regional precipita- Tables Figures tion recycling ratio in the Amazon basin (Table 2) compares well with previous studies using other datasets and methodologies (See Table 1). The spatial patterns of con- J I tinental moisture recycling ratios (Fig. 4d, i, e and j) are slightly different from those J I 20 found by (van der Ent et al., 2010, Figs. 3 and 4) due to the differences in the ver- sions of the model (here we use WAM-2layers) and the datasets used. The continental Back Close precipitation recycling ratio in the Amazon basin reaching 30 % during the Southern Full Screen / Esc Hemisphere summer is compatible with the estimation of 36.4 % found by Bosilovich and Chern (2006). The maps of direct recycling ratios (Fig. 7c, and g, a and e) are Printer-friendly Version 25 in good agreement with maps of regional recycling ratio presented in previous studies (Eltahir and Bras, 1994, Figs. 4 and 6 and Burde et al., 2006, Figs. 2 and 8 and Interactive Discussion Dirmeyer et al., 2009 see http://www.iges.org/wcr/, Moisture Sources by Basin). We note that our analysis period from 2001–2010 includes two major droughts in the Amazon basin (Marengo et al., 2008; Lewis et al., 2011). Because the

17495 icsinPpr|Dsuso ae icsinPpr|Dsuso ae | Paper Discussion | Paper Discussion | Paper Discussion | Paper Discussion land–atmosphere coupling on the hydrological cycles increases during drought years (Bagley et al., 2014), this might inﬂuence the output of the atmospheric moisture track- ACPD ing model used in this study. Analyzing these periods separately is ongoing research. 14, 17479–17526, 2014 3.2 Importance of cascading moisture recycling Cascading moisture 5 Continental moisture recycling is of crucial importance for South American precipitation recycling patterns (Fig. 4). We now quantify this importance and identify intermediary and sink regions of cascading moisture recycling. D. C. Zemp et al.

3.2.1 The dependency on cascading moisture recycling Title Page The share of cascading moisture on total moisture inﬂow is on average 10 % in the Abstract Introduction 10 South American continent. Regions which are dependent on cascading moisture re-

cycling for local rainfall (Fig. 5a and c) are also dominant sinks of moisture from the Conclusions References continent (Fig. 4d and i). We note that cascading moisture contributes more to the precipitation over the Ama- Tables Figures zon basin during the dry season (11 % on average, up to 25 % in the western part) 15 compared to the wet season (8 % on average) (Table 2). The inverse situation is ob- J I served in the La Plata basin, where on average 14 % of the precipitation during the J I dry season and 17 % during the wet season comes from cascading moisture recycling (Table 2). In Sect. 3.4, we reveal the evaporative source of cascading moisture which Back Close

precipitates over the La Plata basin and we understand this seasonal variability. Full Screen / Esc 20 The share of cascading moisture on total moisture inﬂow reaches up to 50 % in the

eastern side of the central Andes (Fig. 5a and c), one of the most vulnerable biodi- Printer-friendly Version versity 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 Interactive Discussion might lead to an over-estimation of the regional recycling process and thus an over- 25 estimation of the importance of cascading moisture recycling.

17496 icsinPpr|Dsuso ae icsinPpr|Dsuso ae | Paper Discussion | Paper Discussion | Paper Discussion | Paper Discussion 3.2.2 The contribution of intermediary regions to cascading moisture recycling ACPD The contribution of evapotranspiration from the Amazon basin to cascading moisture recycling in the continent reaches up to 25 % during the dry season in the central part 14, 17479–17526, 2014 of the Amazon basin and 35 % during the wet season in its southwestern part (Fig. 5b 5 and d). These regions are important intermediaries in cascading moisture recycling Cascading moisture pathways. recycling In order to quantify the importance of these intermediary regions for regional rainfall over the La Plata basin, we quantify the share of the moisture inﬂow in the La Plata D. C. Zemp et al. basin that has cascaded in these regions. This share is 8 % during the wet season and 10 4 % during the dry season. These estimations represent almost half of the share of total moisture inﬂow that has cascaded in the entire continent during the wet season Title Page and one third during the dry season (Table 2). These results mean that the south- Abstract Introduction western part of the Amazon basin is an important intermediary for cascading moisture transported towards the La Plata basin during the wet season. Conclusions References Tables Figures 15 3.3 Complex network analysis

We have shown the importance of cascading moisture recycling for South American J I moisture transport (see Fig. 5). Using the clustering coeﬃcient associated with the J I Middleman motif (C˜ ), we are able to identify intermediary locations involved in cas- Back Close cading moisture recycling as alternative pathways to the direct transport of moisture. 20 These regions are the central part of the Amazon basin during the dry season and the Full Screen / Esc south-western part of the Amazon basin during the wet season (Fig. 6a and c). This is in good agreement with other measures quantifying the contribution of intermediary Printer-friendly Version regions to cascading moisture recycling (Fig. 5b and d). Interactive Discussion The betweenness centrality (B) reveals intermediary regions where cascading mois- 25 ture recycling pathways are channeled. Regions with high B coincide with regions which high C˜ during the wet season (Fig. 6c), but not during the dry season (Fig. 6). This non-overlap is probably explained by the cutting of long-range moisture recycling 17497 icsinPpr|Dsuso ae icsinPpr|Dsuso ae | Paper Discussion | Paper Discussion | Paper Discussion | Paper Discussion pathways in the calculating of the B, as we have shown that the incoming moisture over the La Plata basin during the dry season is mainly transported through direct (and thus ACPD long-range) moisture recycling pathways (Fig. 5a). 14, 17479–17526, 2014 During the wet season, cascading moisture recycling pathways are channeled in the 5 south-western part of the Amazon basin and a narrow band east of the subtropical An- des (Fig. 6d). This observation may be explained by the combined eﬀect of the acceler- Cascading moisture ation of the South American Low Level Jet (Vera et al., 2006) and the high precipitation recycling and evapotranspiration during the wet season (Fig. 4) allowing for an intensive local exchange of moisture between the vegetation and the atmosphere. D. C. Zemp et al.

10 3.4 Direct and cascading moisture recycling from the Amazon basin to the La Plata basin Title Page Abstract Introduction 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 Fig. 4). In the Conclusions References

following, we further investigate the transport mechanism between the two basins. Tables Figures 15 In the La Plata basin, 23 % of the precipitation during the wet season and 25 % during the dry season originated from the Amazon basin through direct moisture recycling J I (Fig. 7c and g and Table 2). This is compatible with the yearly average estimates of 23 % found in Dirmeyer et al. (2009, see http://www.iges.org/wcr/) and 23.9 % found J I

in Martinez et al. (2014). Considering cascading moisture recycling once moisture has Back Close 20 left the Amazon basin (Fig. 2a) increases the dependency from 23 to 29 % during the wet season (Fig. 7h and Table 2). As mentioned above, this might be explained by the Full Screen / Esc high evapotranspiration and precipitation allowing for an exchange of moisture on the way, downwind of the Amazon basin, and by the intensiﬁcation of the SALLJ during Printer-friendly Version

this time of the year (Marengo et al., 2004). This result suggests that the impact of Interactive Discussion 25 deforestation in the Amazonian forest on the moisture supply in the La Plata basin might be larger than expected if only direct transport of moisture between the two basins are considered.

17498 icsinPpr|Dsuso ae icsinPpr|Dsuso ae | Paper Discussion | Paper Discussion | Paper Discussion | Paper Discussion The southern part of the Amazon basin is a direct source of precipitation over the La Plata basin, with a direct contribution reaching 15 % of its evapotranspiration during the ACPD dry season and 35 % during the wet season (Figs. 7a and 7e). This ﬁnding is in agree- 14, 17479–17526, 2014 ment with Martinez et al. (2014) who found that the southern part of the basin is an 5 quasi-permanent direct source of moisture for the La Plata basin. However, if cascading moisture recycling are considered (Fig. 2b), the entire Amazon basin becomes the Cascading moisture evaporative source of moisture over the La Plata basin during the wet season (Fig. 7f). recycling The indirect contribution represents on average 7 % of the total evapotranspiration in the Amazon basin during the wet season (Table 2). This result means that during the D. C. Zemp et al. 10 wet season, the southern part of the Amazon basin is not only a source of moisture but also an intermediary region where moisture originating from the entire basin cascades Title Page on its way to the La Plata basin. This ﬁnding is in agreement with other measures showing intermediary locations involved in cascading moisture recycling (see Sect. 3.2). Abstract Introduction

3.5 Possible impact of land cover change in the intermediary regions Conclusions References Tables Figures 15 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 J I year round and it is in addition an intermediary region for cascading moisture recycling originating from the entire Amazon basin during the wet season (Sect. 3.4). J I

Land cover change in the southern part of the Amazon basin might weaken continen- Back Close 20 tal moisture recycling and might lead to an important decrease in the total precipitation locally and downwind. Among the aﬀected regions, important impacts would be ob- Full Screen / Esc served in particular in the south-western part of the Amazon basin which has already a high probability to experience a critical transition from forest to savanna (Hirota et al., Printer-friendly Version

2011) and in the La Plata basin which is dependent on incoming rainfall for the agri- Interactive Discussion 25 culture (Rockström et al., 2009; Keys et al., 2012). In the eastern side of the central Andes, the impact of an upwind weakening of cascading moisture recycling might be reduced since precipitation in this region is insured by orographic lifting (Figueroa and Nobre, 1990). 17499 icsinPpr|Dsuso ae icsinPpr|Dsuso ae | Paper Discussion | Paper Discussion | Paper Discussion | Paper Discussion 4 Conclusions ACPD 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 14, 17479–17526, 2014 America. We have introduced the concept of “cascading moisture recycling” to refer to 5 moisture recycling between two locations on the continent which involve one or more Cascading moisture re-evaporation cycles along the way. We have proposed measures to quantify the im- recycling portance of cascading moisture recycling and to reveal direct and indirect sources and sinks of moisture for a given region. We have used for the ﬁrst time a complex network D. C. Zemp et al. approach to identify intermediary regions in the cascading moisture recycling path- 10 ways. Using the atmospheric moisture tracking model WAM-2layers (WAM-2 layers) forced Title Page by precipitation from TRMM and evapotranspiration from MODIS in South America, we Abstract Introduction have shown that even if the amount of water transported through cascading moisture recycling pathways is typically smaller than the one transported directly in the atmo- Conclusions References 15 sphere, the contribution by the ensemble of cascading pathways can not be neglected. Tables Figures In fact, 10 % of the total precipitation over South America and 17 % of the precipitation

over the La Plata basin comes from cascading moisture recycling. J I The La Plata basin is highly dependent on moisture from the Amazon basin during both seasons, as 23 % of the total precipitation over the La Plata basin during the J I 20 wet season and 25 % during the dry season comes directly from the Amazon basin. To Back Close these direct dependencies, 6 % of the precipitation during the wet season can be added if cascading moisture recycling outside the Amazon basin are considered. During the Full Screen / Esc dry season, the main source of continental moisture over the La Plata basin is the southern part of the Amazon basin. During the wet season, the southern part of the Printer-friendly Version 25 Amazon basin is not only a source region but is also an intermediary region which Interactive Discussion distributes moisture from the entire Amazon basin into the La Plata basin. Land use change in these regions, which include the arc of deforestation, may weaken moisture

17500 icsinPpr|Dsuso ae icsinPpr|Dsuso ae | Paper Discussion | Paper Discussion | Paper Discussion | Paper Discussion recycling processes and may have stronger consequences for rainfed agriculture and natural ecosystems regionally and downwind as previously thought. ACPD In addition, we showed that the eastern ﬂank of the subtropical Andes – located in 14, 17479–17526, 2014 the pathway of the South American Low Level Jet – plays an important role in the con- 5 tinental moisture recycling as it channels many cascading pathways. This study oﬀers new methods to improve our understanding of vegetation and atmosphere feedback on Cascading moisture the water cycle needed in a context of land use and climate change. recycling

D. C. Zemp et al. Appendix A: Moisture recycling ratios

In these measures the irregular sizes of the portion of the Earth’s surface covered by Title Page 10 the grid cells are taken into account as described in Zemp et al. (2014). Abstract Introduction

A1 Direct moisture recycling ratio Conclusions References

The fraction of precipitation in grid cell j that comes directly from Ω is calculated as: Tables Figures

P m i∈Ω ij J I ρΩ,j = , (A1) Pj J I

15 where mij is the amount of moisture which evaporates in i and precipitates in j and Pj is Back Close the precipitation in j. The fraction of evapotranspiration in grid cell i which precipitates directly in Ω is calculated as: Full Screen / Esc P j∈Ω mij Printer-friendly Version εΩ,i = , (A2) Ei Interactive Discussion

20 where Ei is the evapotranspiration in i.

17501 icsinPpr|Dsuso ae icsinPpr|Dsuso ae | Paper Discussion | Paper Discussion | Paper Discussion | Paper Discussion A2 Cascading moisture recycling ratio ACPD To calculate the cascading moisture recycling ratios as deﬁned in Sect. 2.3.2, we calculate the individual contributions of cascading moisture recycling pathways consisting 14, 17479–17526, 2014 of k re-evaporation cycles (k ∈ {1,...,n}) which add up to the total cascading moisture 5 recycling contribution. We chose a maximum number of cycles n = 100, while the con- Cascading moisture tribution of pathways with number of cycles larger than 3 are close to zero. If we track recycling moisture forward in space, we have to take into account that moisture is lost as runoﬀ on the way during the cascading recycling. This is not the case for moisture backward D. C. Zemp et al. tracking in space because we quantify the remaining amount of moisture that actually 10 arrives at destination. Title Page A2.1 Cascading precipitation recycling ratio Abstract Introduction

The fraction of precipitation in grid cell j that comes from Ω through cascading moisture Conclusions References recycling involving one re-evaporation cycle is: Tables Figures P (1) i6∈Ω mji · ρΩ,i ρ = , (A3) Ω,j P J I 15 j J I where ρ is the fraction of precipitation in j that comes directly from Ω (Sect. A1). Ωj Following the same principle as in Eq. (A3), the fraction of precipitation in j that comes Back Close from Ω through cascading moisture recycling involving n re-evaporation cycles is: Full Screen / Esc

n P m · ρ( −1) (n) i6∈Ω ij Ω,i Printer-friendly Version ρ = , (A4) Ω,j P 20 j Interactive Discussion

n where ρ( −1) is the fraction of precipitation in i that comes from through cascading Ω,i Ω moisture recycling involving n − 1 re-evaporation cycles. The total fraction of precipitation in j that comes from Ω through cascading moisture recycling is the sum of all 17502 icsinPpr|Dsuso ae icsinPpr|Dsuso ae | Paper Discussion | Paper Discussion | Paper Discussion | Paper Discussion individual contributions of cascading recycling:

n ACPD ρcasc ρ(1) ... ρ( ) . (A5) Ω,j = Ω,j + + Ω,j 14, 17479–17526, 2014 A2.2 Cascading evapotranspiration recycling ratio Cascading moisture 5 The fraction of evapotranspiration in grid cell i that contributes to precipitation over Ω through cascading moisture recycling involving one re-evaporation cycle is: recycling P D. C. Zemp et al. j6∈Ω mij · εΩ,j · αj ε(1) , (A6) Ω,i = Ei

where εΩ,j is the fraction of evapotranspiration in j which precipitates directly over Ω Title Page 10 (Sect. A1) and α = E /P . Similarly, the fraction of evapotranspiration in i that precip- j j j Abstract Introduction itates over Ω through cascading moisture recycling involving n re-evaporation cycles is: Conclusions References n P m · ε( −1) · α Tables Figures n j6∈Ω ij Ω,j j ε( ) , (A7) Ω,i = Ei J I (n−1) 15 where ε is the fraction of evapotranspiration in j that precipitates over through Ω,j Ω J I cascading moisture recycling involving n−1 re-evaporation cycles. The total fraction of Back Close evapotranspiration in i that precipitates over Ω through cascading moisture recycling is the sum of the individual contribution of cascading recycling: Full Screen / Esc

(1) (n) εcasc = ε + ... + ε (A8) 20 Ω,i Ω,i Ω,i Printer-friendly Version

Interactive Discussion Appendix B: Quantifying cascading moisture recycling

To quantify the contribution of cascading moisture recycling to total moisture in- and outﬂow, we remove the re-evaporation of moisture from continental origin. By doing so, 17503 icsinPpr|Dsuso ae icsinPpr|Dsuso ae | Paper Discussion | Paper Discussion | Paper Discussion | Paper Discussion we inhibit all cascading recycling of moisture from continental origin in the network (see Fig. B1). To achieve this, we derive for each grid cell the evaporation of moisture from ACPD oceanic origin (i.e., that has been last evaporated over the ocean) as in Eq. (1): 14, 17479–17526, 2014 E E = i · P , (B1) i←ocean P i←ocean 5 i Cascading moisture where Pi←ocean is the precipitation from oceanic origin in i (Pj←ocean = Pj − Pj←continent recycling P and Pj←continent = i∈continent mij .). Using the same assumption, we get the moisture transport between each pair of grid cells i and j that results from evaporation of mois- D. C. Zemp et al. ture from oceanic origin only:

mij Title Page 10 mij←ocean = · Ei←ocean, (B2) Ei Abstract Introduction At this stage, mij←ocean can be interpreted as the evapotranspiration in i which precipitates in j and which has been evaporated from the ocean before that (mij←ocean < mij ). Conclusions References In a second step, we derive the corresponding moisture in- and outﬂow from or to- Tables Figures 15 wards a given region Ω for each grid cell: X Pj←Ω,o = mij←ocean (B3a) J I i∈Ω X J I Ei→Ω,o = mij←ocean. (B3b) Back Close j∈Ω Full Screen / Esc Pj←Ω,o can be interpreted as the precipitation in j originating from the re-evaporation 20 of oceanic moisture in Ω. Similarly, Ei→Ω,o can be seen as the evapotranspiration of oceanic moisture in i which precipitates over Ω. Printer-friendly Version

Thus, are able to derive the corresponding reduction in total moisture inﬂow towards Interactive Discussion Ω or outﬂow from Ω:

∆Pj←Ω = Pj←Ω − Pj←Ω,o (B4a)

25 ∆Ei→Ω = Ei→Ω − Ei→Ω,o, (B4b) 17504 P | Paper Discussion | Paper Discussion | Paper Discussion | Paper Discussion where Pj←Ω = i∈ mij is the total precipitation in j originating from Ω and Ej→Ω = P Ω j∈Ω mij is the total evapotranspiration in i which contributes to precipitation over Ω. ACPD Thus, ∆P is the precipitation in j originating from the re-evaporation of continen- j←Ω 14, 17479–17526, 2014 tal moisture in Ω and ∆Ei→Ω is the re-evaporation of continental moisture in i which 5 precipitates over Ω. If Ω is the entire South American continent (resp. the intermediary region), ∆Pj←Ω be- Cascading moisture comes ∆Pc (resp. ∆Pm) and ∆Ei→Ω becomes ∆Ec (resp. ∆Em) as deﬁned in Sect. 2.4. recycling D. C. Zemp et al. Appendix C: Complex network analysis

C1 Clustering coeﬃcient associated with Middleman motifs Title Page

Abstract Introduction 10 Mathematically, the clustering coeﬃcient C of the grid cell i is:

Conclusions References ti Ci = , (C1) Ti Tables Figures

where ti is the number of Middleman motifs that i forms and Ti is the total number of that motif that i could have formed according to its number of incoming and outgoing J I

15 arrows. To give more weight to a motif involved in the transport of a larger amount J I 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 Back Close arrows. The weighted counterpart of Eq. (C1) is: Full Screen / Esc t˜ ˜ i Ci = , (C2) Printer-friendly Version 20 Ti Interactive Discussion with t˜i the weighted counterpart of ti (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, Table 1) and has been corrected in order to account for the 17505 icsinPpr|Dsuso ae icsinPpr|Dsuso ae | Paper Discussion | Paper Discussion | Paper Discussion | Paper Discussion irregular sizes of the portion of the Earth’s surface covered by the grid cells as explained T in (Zemp et al., 2014). The numerator of Eq. (C2) can be derived as t˜i = (PP P)ii with ACPD 1/3 P = {pij }i,j∈N and pij is the weight of the arrow originating from i and pointing towards 14, 17479–17526, 2014 j. Here, in order to avoid a strong correlation between the clustering coefficient and the 2 5 mean evapotranspiration and precipitation, we chose this weight to be pij = mij /(Ei Pj ). in out in Cascading moisture The denominator of Eq. (C2) is Ti = ki ki where ki is the number of arrows pointing recycling out towards i and ki the number of arrows originating from i: D. C. Zemp et al. in X ki = aji , (C3a) j=6 i Title Page out X ki = aij , (C3b) Abstract Introduction 10 j=6 i Conclusions References where aij = 1 if there is an arrow originating from i and pointing towards j and aij = 0 otherwise. In order to compare the results for the two seasons, we normalize C˜ with Tables Figures the maximum observed value for each network. J I C2 Optimal pathways and betweenness J I

15 C2.1 Optimal pathway Back Close

In complex network theory, many centrality measures (e.g. closeness and between- Full Screen / Esc ness) are based on the concept of a shortest path. The shortest path is usually defined as the pathway between nodes which has the minimum cost. In this work, it is defined Printer-friendly Version as the pathway which contributes most to the moisture transport between two grid cells. Interactive Discussion 20 As this pathway is not necessarily the shortest one in term of geographical distance, we will call it “optimal pathway” to avoid confusion. Let (t1,t2,...,tn) be the intermediary grid cells in a cascading moisture recycling pathway from grid cell i to grid cell j. The contribution of this pathway is defined as the 17506 icsinPpr|Dsuso ae icsinPpr|Dsuso ae | Paper Discussion | Paper Discussion | Paper Discussion | Paper Discussion fraction of precipitation in j that comes from evapotranspiration in i through cascading moisture recycling: ACPD m n−1 m m 14, 17479–17526, 2014 it1 Y tl tl+1 tnj W = · · (C4) i,t1,...,tn,j P P P t tl j 1 l=1 +1 Cascading moisture

5 An example of pathway contributions is provided in Fig. B1. The contribution of each recycling existing pathway is calculated between any pair of grid cells in the network. The optimal D. C. Zemp et al. pathway 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, Title Page 10 the cost of a pathway is calculated as the sum of the weight of its arrows. In order to adapt the method to our purpose, we chose the weight of the arrows as w = Abstract Introduction tl tl+1 m tl tl+1 −log( P ). The cost of a pathway from grid cell i to grid cell j as calculated in iGraph Conclusions References tl+1 becomes: Tables Figures n−1 0 X W = w1t + wt t + wt j J I i,t1,...,tn,j 1 l l+1 n l=1 J I m n−1 m m it1 X tl tl+1 tnj 15 = −log( ) − log( ) − log( ) Back Close P P P t1 l=1 tl+1 j 1 Full Screen / Esc = log( m m m ) 1t1 Qn−1 tl tl+1 tnj P · l=1 ( P ) · P Printer-friendly Version t1 tl+1 j 1 = log( ) Interactive Discussion W i,t1,...,tn,j Because the optimal pathway is defined as the pathway with the minimum cost W 0, it 20 corresponds to the pathway with the maximum contribution W as defined above. 17507 icsinPpr|Dsuso ae icsinPpr|Dsuso ae | Paper Discussion | Paper Discussion | Paper Discussion | Paper Discussion C2.2 Betweenness centrality ACPD Mathematically, betweenness of the grid cell i is the fraction of the number of optimal pathways between any pair of grid cells which pass through i: 14, 17479–17526, 2014

σ (i) X jk Cascading moisture Bi = (C5) σjk recycling 5 j,k D. C. Zemp et al. with σjk is the number of optimal pathways between grid cells j and k, and σjk (i) is the number of these pathways that pass through the grid cell i. B reaches values between N−1 2 0 and 2 = (N −3N +2)/2 with N the number of grid cells. To calculate it, we used Title Page

the directed and weighted version of the method betweenness in the package iGraph Abstract Introduction 10 for Python. The choice of the weights used in this method is explained in Sect. C2.1. Conclusions References

Author contribution Tables Figures

J. F. Donges, H. M. J. Barbosa, C.-F. Schleussner and D. C. Zemp developed the analy- J I 15 sis. R. J. Van der Ent, performed the simulation of WAM-2layers. G. Sampaio provided the mask of the La Plata basin. D. C. Zemp performed the analysis and prepared J I the manuscript with contributions from all co-authors. C.-F. Schleussner conceived the Back Close project together with J. Heinke and supervised it together with A. Rammig. Full Screen / Esc Acknowledgements. This paper was developed within the scope of the IRTG 1740/TRP 20 2011/50151-0, funded by the DFG/FAPESP. J. Donges acknowledges funding from the Printer-friendly Version Stordalen Foundation and BMBF (project GLUES) and R. J. van der Ent from NWO/ALW. We thank K. Thonicke for comments on the manuscript and P. Manceaux for his help on designing Interactive Discussion the network schemes.

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Cascading moisture Table 1. Overview of regional precipitation recycling ratio in the Amazon basin as found in recycling many studies. Abbreviations: the European Centre for Medium-Range Weather Forecasts (ECMW); Geophysical Fluid Dynamics Laboratory Precipitation (GFDL); Climate Prediction D. C. Zemp et al. 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 Title Page by the National Center for Atmospheric Research (NCAR). Abstract Introduction Study Method Dataset Period Precipitation recycling ratio (Brubaker et al., 1993) Atmospheric Bulk model GFDL and NCAR 1963–1973 24 Conclusions References (Eltahir and Bras, 1994) Atmospheric Bulk model ECMWF reanalysis 1985–1990 25 GFDL 1963–1973 35 (Trenberth, 1999) Atmospheric Bulk model CMAP and NCEP-NCAR reanalysis 1979–95 34 Tables Figures (Bosilovich and Chern, 2006) AGCM with water vapor IC from the model 1948–1997 27.2 during OND tracers (Burde et al., 2006) Atmospheric Bulk model DAO 1981–1993 31 (general) J I Atmospheric Bulk model 26 (Budyko model) J I Atmospheric Bulk model 41 (IMB) (Dirmeyer et al., 2009) Quasi-isentropic DOE reanalysis 1979–2003 10.8 for area 106 km2 Back Close back-trajectory method (van der Ent et al., 2010) Atmospheric moisture ERA-Interim reanalysis 1999–2008 28 Full Screen / Esc tracking model Zemp et al. (this study) Atmospheric moisture TRMM and MODIS 2001–2010 28 tracking model Printer-friendly Version

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Table 2. Results (in %) averaged for the La Plata basin, the Amazon basin and for the South American continent during the wet season (DJFM), the dry season (JJAS) and all year round. Cascading moisture recycling Notation Description La Plata basin Amazon basin South America wet dry year wet dry year wet dry year D. C. Zemp et al. ρc Fraction of precipitation originating from evap- 42 35 41 30 35 32 30 29 31 otranspiration from the continent ρAm Fraction of precipitation originating from evap- 23 25 24 26 30 28 18 21 20 otranspiration from the Amazon basin through Title Page direct moisture recycling ρcasc Am Fraction of precipitation originating from evap- 6 2 4 – – – 11 6 8 Abstract Introduction otranspiration from the Amazon basin through cascading moisture recycling Conclusions References εc Fraction of evapotranspiration that contributes 43 16 35 77 45 65 56 31 47 to precipitation over the continent Tables Figures εPl Fraction of evapotranspiration that contributes 32 12 26 16 7 11 15 7 12 to precipitation over the La Plata basin through direct moisture recycling casc J I εPl Fraction of evapotranspiration that contributes – – – 7 3 5 4 1 3 to precipitation over the La Plata basin J I through cascading moisture recycling Back Close ∆Pc/P Fraction of precipitation that comes from cas- 17 14 17 8 11 10 10 9 10 cading moisture recycling on the continent

∆Pm/P Fraction of precipitation that comes from cas- 8 4 6 4 6 5 4 4 4 Full Screen / Esc cading moisture recycling in the intermediary region Printer-friendly Version ∆Ec/E Fraction of evapotranspiration that is involved 11 9 9 11 24 12 13 15 10 in cascading moisture recycling Interactive Discussion

17517 4 | Paper Discussion | Paper Discussion | Paper Discussion | Paper Discussion Zemp et al.: Cascading moisture recycling ACPD otranspiration,14, 17479–17526, particularly 2014 in warm climates and for shallow rooted plants (Savenije, 2004). However, in seasonal forests with deepCascading rooted trees, moisture the moisture which is evaporated dur- recycling 290 ing the dry season can be hold back for one or several months (Savenije,D. 2004). C. Zemp The et al. second condition is fulﬁlled if the soil water at the beginning has the same composition (in term of

tagged fraction)Title asPage the atmospheric moisture at the end of the

season. Abstract Introduction

Conclusions References 295 2.3 Moisture recycling ratio Tables Figures In this section, we define measures to track moisture forward or backwardJ in spaceI from a given region. In the case of a forward tracking,J theI measures indicate the destination (precipitative sink)Back of evaporationClose from the region. In the case Figure 1. Scheme of the moisture recycling network. Nodes 1,2,3,4 represent different grid cells and arrows indicate the direction and amount of moisture originating from evapotranspo-300 of a backwardFull Screen tracking, / Esc they indicate the origin (evaporative ration inFig. the source 1: Scheme cell and contributing of the moisture to precipitation recycling in the target network. cell. For example, Nodes the total source) of precipitation over the region. We first consider E m m Printer-friendly Version evapotranspiration1,2,3,4 represent in 2 ( 2) splits different up in three grid branches: cells and23 precipitates arrows indicate in 3, 24 precipitates the in 4 and m22 is locally recycled. m22 contributes together with m12 to the total precipitation in 2 direct moisture recycling only (Sect. 2.3.1). We then track P direction and amount of moisture originating from evapo- Interactive Discussion ( 2). moisture further forward or backward in space through cas- transporation in the source cell and contributing o precipi- cading moisture recycling (Sect. 2.3.2). Considered together, tation in the target cell. For example, the total evapotranspi- 305 the direct and cascading moisture recycling ratios provide a ration in 2 (E2) splits up in three branches: m23 precipitates 17518 full picture of the sources and sinks of moisture from a region in 3, m24 precipitates in 4 and m22 is locally recycled. m22 of interest. contributes together with m12 to the total precipitation in 2 (P2). 2.3.1 Direct moisture recycling ratios

We define the direct precipitation recycling ratio as the frac- 2.2 Basic assumptions 310 tion of precipitation in each grid cell i that is originating from evapotranspiration from Ω through direct moisture recycling: In order to track moisture forward or backward from a given region Ω which can be of any shape and scale (grid cell, basin, continent), we assume that the moisture composition Pi←Ω ρΩ,i = , (2) 265 within the surface reservoir and the atmosphere for each grid Pi cell remains the same. This implies that, in each grid cell, the tagged fraction of precipitation is linearly proportional to the where Pi←Ω is the amount of precipitation in i that is origi- tagged fraction of evapotranspiration and the tagged fraction 315 nating from evapotranspiration from Ω through direct mois- of transported moisture: ture recycling and Pi is the total precipitation in i (see also Appendix A1). ρΩ quantifies the dependency on direct mois- PΩ EΩ mΩ ture recycling from Ω for local rainfall. High values indicate 270 = = , (1) P E m locations which receive moisture (direct precipitative sink) 320 from Ω. We note that ρ averaged over all grid cells in Ω where E is the total evapotranspiration, P is the total precipi- Ω gives the regional recycling ratio, i.e, the fraction of precip- tation, m is the transported moisture towards or from another itation that is regionally recycled (Eltahir and Bras, 1994; grid cell, P is the tagged fraction of precipitation, E is the Ω Ω Burde et al., 2006; van der Ent and Savenije, 2011). tagged fraction of evapotranspiration and m is the tagged Ω We also define the direct evapotranspiration recycling ra- 275 fraction of transported moisture towards or from another grid 325 tio as the fraction of evapotranspiration in each grid cell i cell. We call “tagged fraction” the share of the moisture orig- that contributes to precipitation over Ω through direct mois- inating from Ω in the case of a backward tracking and the ture recycling: share of moisture precipitating over Ω in the case of a forward tracking. Ei→Ω 280 This assumption is valid under two conditions: (1), evapo- εΩ,i = , (3) Ei transpiration follows directly after the precipitation event or (2), the fraction of tagged moisture in the surface reservoir where Ei→Ω is the amount of evapotranspiration in i that and the atmosphere can be assumed to be temporally constant 330 contributes to precipitation over Ω through direct moisture (i.e., in steady state) (Goessling and Reick, 2013). The first recycling and Ei the total evapotranspiration in i (see also 285 condition is usually fulfilled during interception and fast tran- Appendix A1). εΩ quantifies the local contribution to precip- spiration which are important components of the total evap- itation over Ω through direct moisture recycling. High values icsinPpr|Dsuso ae icsinPpr|Dsuso ae | Paper Discussion | Paper Discussion | Paper Discussion | Paper Discussion Zemp et al.: Cascading moisture recycling 5 ACPD 14, 17479–17526, 2014 indicate locations which distribute moisture (direct evapora- Cascading moisture 335 tive source) over Ω. recycling If Ω is the entire South American continent, ε becomes Ω D. C. Zemp et al. the continental evapotranspiration recycling ratio (εc) and ρΩ the continental precipitation recycling ratios (ρc) as defined Title Page in van der Ent et al. (2010). Considered together, εc and ρc Abstract Introduction 340 indicate respectively sources and sinks of continental moisture. In this study we neglect possible contributions of mois- Conclusions References ture in South America from and to other continents, since Tables Figures these contributions to the overall moisture budget are small J I

(van der Ent et al., 2010, Table 2). J I (a) (b) 345 To study the direct moisture recycling between the Ama- Back Close zon basin and the La Plata basin (defined by the red bound- Figure 2. Scheme of cascading moisture recycling (a) for moisture originating from the Amazon Full Screen / Esc basinFig. and 2:(b) Schemefor moisture of that cascading has final destination moisture the La recycling Plata basin. (a) In both for mois-figures, the aries in Fig. 7), we use ρΩ with Ω being all grid cells covering amount of precipitation in grid cell 3 that is originating from evapotranspiration in grid cell 1 is ture originating from the Amazon basin and (b) for moisture Printer-friendly Version the Amazon basin (ρAm) and εΩ with Ω being all grid cells m23 · m12/P2. that has final destination the La Plata basin. In both figures, Interactive Discussion covering the La Plata basin (ε ). While ρ is useful to P l Am the amount of precipitation in grid cell 3 that is originating 350 track moisture from the Amazon basin as a whole, ε pro- P l from evapotranspiration in grid cel 1 is m · m /P . vides information regarding the spatial heterogeneity of the 23 12 2 contribution inside the Amazon basin. 17519 The direct recycling ratios underestimate the strength of the relationship, in term of moisture recycling, between two pathways of cascading moisture recycling. To avoid this, we 355 specific locations. In fact, moisture can be exchanged not only track moisture that crosses the border of Ω. This implies only through direct moisture recycling, but also through cas- 385 that we consider re-evaporation cycles outside Ω only (Fig. cading moisture recycling. 2, see also Appendix A2). To study the cascading moisture recycling between the casc 2.3.2 Cascading moisture recycling ratios Amazon basin and the La Plata basin, we use ρΩ with Ω casc being all grid cells covering the Amazon basin (ρAm ) and We define the cascading precipitation recycling ratio as the casc 390 εΩ with Ω being all grid cells covering the La Plata basin 360 fraction of precipitation in each grid cell i that is originating casc casc (εP l ). While ρAm considers cascading moisture recycling from evapotranspiration from Ω through cascading moisture for moisture originating from the Amazon basin (see Fig. 2a), recycling: casc εP l provides information regarding the importance of cas- casc cading moisture recycling for moisture that has final destina- casc Pi←Ω ρΩ,i = , (4) 395 tion the La Plata basin (see Fig. 2b). Pi Considered together, the direct and cascading recycling ra- casc where Pi←Ω is the amount of precipitation in i that is orig- tios provide a full picture of the origin and destination of casc 365 inating from evapotranspiration from Ω through cascading moisture from a given region. High values of ρAm and ρAm casc moisture recycling. ρΩ quantifies the dependency on cas- indicate together the precipitative sink region of moisture casc cading moisture recycling from Ω for local rainfall. High val- 400 from the Amazon basin and high values of ρAm and ρAm ues indicate the final destination of moisture from Ω after one highlight evaporative source regions of precipitation over the ore more re-evaporation cycles (indirect precipitative sink) . La Plata basin. 370 We also define the cascading evapotranspiration recycling ratio as the fraction of evapotranspiration in each grid cell 2.4 Quantifying cascading moisture recycling i which contributes to precipitation in Ω through cascading moisture recycling as: In this section, we are interested in the importance of cascad- Ecasc 405 ing moisture recycling for the total moisture inflow (precipi- εcasc = i→Ω , (5) tation) and outflow (evapotranspiration). To quantify this, we Ω,i E i forbid re-evaporation of moisture originating from the conti- casc 375 where Ei→Ω is the amount of evapotranspiration in i that nent and we estimate the resulting reduction in total moisture contributes to precipitation over Ω through cascading mois- inflow (∆Pc) and outflow (∆Ec) (see Appendix B). ∆Pc/P casc ture recycling. εΩ quantifies the local contribution to pre- 410 is the fraction of precipitation that comes from cascading cipitation over Ω through cascading moisture recycling. High moisture recycling on the continent, i.e., that has been evap- values indicate locations where moisture initially originated orated at least twice on the continent. It quantifies the de- 380 (indirect evaporative source) before it is distributed over Ω. pendency on cascading moisture recycling for local rainfall. The moisture inflow (resp. outflow) that crosses the border ∆Ec/E is the fraction of total evapotranspiration that is in- of Ω may be counted several times as it is involved in several 415 volved in cascading moisture recycling on the continent, i.e., icsinPpr|Dsuso ae icsinPpr|Dsuso ae | Paper Discussion | Paper Discussion | Paper Discussion | Paper Discussion ACPD 14, 17479–17526, 2014 6 Zemp et al.: Cascading moisture recycling Cascading moisture ternative torecycling the direct recycling of moisture between sources and sinks.D. We C. Zemp compute et al. the weighted version of the cluster- 450 ing coefficient (C˜) (Fagiolo, 2007; Zemp et al., 2014) for

each grid cellTitle as Page described in the Appendix C1. A grid cell ˜ has a highAbstractC if itIntroduction fulfills two conditions: (1) it is the intermediary location in a high number of Middleman motifs and Conclusions References (2) each arrow involved in the motifs has a great through- Tables Figures 455 put. C˜ is equal to zero if the grid cell forms no Middleman FigureFig. 3. Scheme 3: Scheme of two possible of two patterns possible in the patterns Middleman in motif the from Middleman the perspective of motif at all.J In our study,I regions which have a larger cluster- grid cell 1. The grid cell 1 (dark gray) receives and distributes moisture from and to grid cells ing coefficient than the 80 percentile are called “Middleman 2 andmotif. 3 (light gray) The which grid also cell exchange1 (dark moisture gray) such receives that there and is no distributes cyclic relation. The J I m regions”. exchangemoisture of moisture from between and 2 to and grid 3 uses cells two alternative 2 and 3 pathways: (light gray) the direct which one ( 23 in Back Close m m m m m (a) or 32 in (b)) and the cascading pathway ( 21 13 in (a) or 31 12 in (b)). The grid cell 1 is It is worth to note that the Middleman motif considers an intermediaryalso exchange on an alternative moisture pathway such to the that direct there transport is no of moisture cyclic between relation. 2 and 3. Full Screen / Esc The exchange of moisture between 2 and 3 uses two alterna- 460 three interconnected grid cells which corresponds to cascading moisturePrinter-friendly recycling Version pathways involving only one re- tive pathways: the direct one (m23 in (a) or m32 in (b)) and evaporationInteractive cycle. Discussion These pathways contribute usually most to the cascading pathway (m21m13 in (a) or m31m12 in (b)). The grid cell 1 is an intermediary on an alternative pathway moisture transport between two locations. In fact, the amount to the direct transport of moisture between 2 and 3. of moisture transported in a pathway typically decreases with 465 the number of re-evaporation cycles involved in the pathway. 17520 Other motifs formed by three or more grid cells linked by that comes from the continent and that further precipitates moisture recycling exist (Zemp et al., 2014), but are not ana- over the continent. It quantifies the contribution of a specific lyzed here. location to cascading moisture recycling. In addition, we are interested in the importance of cascad- 2.5.2 Betweenness Centrality 420 ing moisture recycling in the Middleman region (see Sect.

2.5.1) for the total moisture in- and outflow. We use the same 470 The betweenness centrality (B) aims to highlight nodes in approach as above. We forbid re-evaporation in the Middle- the network with central position “to the degree that they man region of moisture originating from the continent and stand between others and can therefore facilitate, impede or we estimate the resulting reduction in total moisture inflow bias the transmission of messages” in the network (Freeman, 425 (∆Pm) (see Appendix B). ∆Pm/P is the fraction of total 1977, p. 36). Here, we use it to reveal intermediary grid cells moisture inflow that comes from cascading moisture recy- 475 where cascading moisture recycling pathways are channeled. cling in the Middleman region. It can be seen as the fraction To compute it, we first identify for each pair of grid cells of precipitation that comes from the continent and that has the moisture recycling pathways with the greatest through- been re-evaporated in the Middleman region. It quantifies the put, called ”optimal pathways”. These pathways can include 430 dependency on cascading moisture recycling in the Middle- any number of re-evaporation cycles. As the optimal path- man region for local rainfall. 480 way is usually the direct one (without any re-evaporation cycle), we first had to modify the network such that the optimal 2.5 Complex network analysis pathways involve cascading moisture recycling. To do so, we removed from the network all long-range moisture transport, We investigate important moisture recycling pathways using i.e, occurring over distances larger than 15 geographical de- two measures from complex network analysis: clustering co- 485 grees. The choice of this threshold does not influence the re- 435 efficient associated with Middleman motifs and betweenness sults qualitatively. Once optimal pathways are identified, we centrality. find intermediary grid cells that they have in common (see Appendix C2). A grid cell has a high B if many optimal path- 2.5.1 Middleman motifs and clustering coefficient ways pass through it and has a B equal to 0 if none of these 490 pathways pass through it, i.e., moisture never cascades in the In complex network theory, motifs are defined as significant grid cell. and recurring patterns of interconnections that occur in the 440 network (Milo et al., 2002). Here, a grid cell forms a Mid- dleman motif (Fagiolo, 2007) if is an intermediary on an al- 2.5.3 Similarities and differences between the Between- ternative pathway to the direct transport of moisture between ness Centrality and the Middleman motif two other grid cells (Fig. 3). The clustering coefficient (C) is a measure from complex We expect similar spatial patterns in the results of the be- 445 network analysis which measures the tendency to form a par- 495 tweenness centrality (Sect. 2.5.2) and the clustering coeffi- ticular motif (Fagiolo, 2007). Here, it reveals intermediary cient associated with the Middleman motifs (Sect. 2.5.1). In locations in cascading moisture recycling pathways, as the al- fact, both measures reveal important intermediary grid cells icsinPpr|Dsuso ae icsinPpr|Dsuso ae | Paper Discussion | Paper Discussion | Paper Discussion | Paper Discussion 8 Zemp et al.: Cascading moisture recycling

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(a) Precip. (b) Evap. (c) Evap. - Precip. (d) ρc (e) εc Title Page Wet season Abstract Introduction

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J I (f) Precip. (g) Evap. (h) Evap. - Precip. (i) ρc (j) εc

Fig. 4: Long term seasonal mean of precipitation (a,f), evapotranspiration (b,g), precipitation - evapotranspiration (c,h) for the Back Close Figure 4.periodLong 2001-2010 term as calculated seasonal from TRMMmean and of MODIS. precipitation Continental precipitation(a, f), evapotranspiration recycling ratio ρc (e,j) and continental(b, g), precip- evapotranspiration recycling ratio εc (d,i) showing respectively sinks and sources of continental moisture. Here and in the Full Screen / Esc itation –following evapotranspiration figures, the vectors indicate(c, h) thefor horizontal the moisture period flux 2001–2010 field in m3ofmoisture/ as calculated(m2 · month) and from the hatches TRMM and represent grid cells where annual mean evapotranspiration exceeds mean annual precipitation. Results are given during the dry MODIS. Continental precipitation recycling ratio ρc (d, i) and continental evapotranspiration season (JJAS) (upper row) and the wet season (DJFM) (lower row). recycling ratio εc (e, j) showing respectively sinks and sources of continental moisture. Here Printer-friendly Version and in the following figures, the vectors indicate the horizontal moisture flux field (in m3 of 600 portant− impacts2 would be− observed1 in particular in the south- 615 cascading moisture recycling might be reduced since precipi- Interactive Discussion moisturewestern× m part× ofmonth the Amazon) basin and which the has hatches already a high representtation in this grid region cells is insured where by orographic annual lifting (Figueroa mean evapo- transpirationprobability exceeds to experience mean a critical annual transition precipitation. from forest to and Results Nobre, 1990). are given for the dry season (JJAS) savanna (Hirota et al., 2011) and in the La Plata basin which (upper row)is dependent and the of incoming wet season rainfall for the (DJFM) agriculture (lower (Rock- row).3.3 Complex network analysis 605 strom¨ et al., 2009; Keys et al., 2012). The share of cascading moisture on total moisture inflow 3.3.1 Middleman motif reaches up to 50% in the eastern side of the central Andes (Figs. 5a and 5c), one of the most vulnerable biodiversity17521620 Cascading moisture recycling plays an important role for hotspots on Earth (Myers et al., 2000). However, this latter South American moisture transport (see Fig. 5). Using the clustering coefficient (C˜) associated with the Middleman 610 observation should be considered with caution due to the imbalance of the water cycle in this area which might lead to motif, we are able to identify intermediary locations involved an over-estimation of the regional recycling process and thus in cascading moisture recycling as alternative pathways to an over-estimation of the importance of cascading moisture 625 the direct transport of moisture. These regions (called Mid- recycling. In addition, the impact of an upwind weakening of dleman regions) are the central and western part of the Ama- zon basin during the dry season and the south-western part Zemp et al.: Cascading moisture recycling 9 icsinPpr|Dsuso ae icsinPpr|Dsuso ae | Paper Discussion | Paper Discussion | Paper Discussion | Paper Discussion

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(a) ∆Pc/P (b) ∆Ec/E (a) C˜ (b) B Wet season (DJFM) Wet season (DJFM) Abstract Introduction

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˜ (c) ∆P /P (d) ∆E /E (c) C (d) B c c Printer-friendly Version Fig. 6: Complex network analysis. Clustering coefﬁcient C˜ Figure 5. Fraction of totalFig. precipitation 5: Fraction of totaloriginating precipitation from originating cascading from cas- moisture recycling (∆P /P ) cading moisture recycling (∆Pc/P ) (a,c) and fraction of to- associated with the motifc Middleman (a,c) and BetweennessInteractive Discussion (a, c) and fraction of totaltal evapotranspiration evapotranspiration that isthat involved is in involved cascading inmoisture cascadingCentrality moistureB (b,d).recycling While high values of C˜ indicate interme- recycling (∆E /E) (b,d). While high values of ∆P /P in- diary locations where cascading moisture recycling allows (∆Ec/E) (b, d). While high values of ∆c Pc/P indicate regions whichc are dependent on cascading dicate regions which are dependent of cascading moisture for alternative pathways to the direct transport of moisture, moisture recycling for local rainfall, high values of ∆Ec/E indicate intermediary regions which recycling for local rainfall, high values of ∆Ec/E indicate high values of B indicate regions where pathways of cascad- contribute to cascading moistureregions which recycling. contribute to cascading moisture recycling. ing moisture recycling are channeled. Results are given for the dry season (upper row) and the wet season (lower row). 17522

of the Amazon basin during the wet season. This is in good (Table 42). These results imply that the Middleman regions agreement with other measures quantifying the contribution are important intermediary regions involved in the alternative 630 of evapotranspiration within cascading moisture recycling 640 pathways to the direct transport of moisture from the Ama- (Figs. 5b and 5d). zon basin to the La Plata basin. In the La Plata basin, the fraction of precipitation that comes from cascading moisture recycling in the Middleman 3.3.2 Betweenness Centrality region is 8% during the wet season and 5% during the dry 635 season. This represents 47% of the fraction of precipitation Cascading moisture recycling pathways are channeled in the that comes from cascading moisture recycling in the conti- south-western part of the Amazon basin and a narrow band nent during the wet season and 35% during the dry season 645 east of the subtropical Andes (Figs. 6b and 6d). Regions with Zemp et al.: Cascading moisture recycling 9 icsinPpr|Dsuso ae icsinPpr|Dsuso ae | Paper Discussion | Paper Discussion | Paper Discussion | Paper Discussion

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Title Page (a) ∆Pc/P (b) ∆Ec/E (a) C˜ (b) B Wet season (DJFM) Wet season (DJFM) Abstract Introduction

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Full Screen / Esc C˜ (d) B (c) ∆Pc/P (d) ∆Ec/E (c)

Fig. 5: Fraction of total precipitation originating from cas- Fig. 6: Complex network analysis. Clustering coefﬁcient C˜ C˜ Printer-friendly Version cading moisture recyclingFigure (∆Pc/P ) (a,c) 6. andComplex fraction of network to- associated analysis. with the Clustering motif Middleman coe (a,c)ﬃcient and Betweennessassociated with the motif Mid- Centrality B (b,d). While high values of C˜ indicate interme- ˜ tal evapotranspiration thatdleman is involved(a, in cascading c) and moisture betweenness centrality B (b, d). While high values of C indicate intermedi- Interactive Discussion diary locations where cascading moisture recycling allows recycling (∆Ec/E) (b,d).ary While locations high values whereof ∆Pc/P cascadingin- moisture recycling allows for alternative pathways to the direct dicate regions which are dependent of cascading moisture for alternative pathways to the direct transport of moisture, recycling for local rainfall,transport high values of of ∆ moisture,Ec/E indicate highhigh values values of of B indicateindicate regions regions where pathways where of pathways cascad- of cascading moisture regions which contribute torecycling cascading moisture are channeled. recycling. Resultsing moisture are recycling given are for channeled. the dry Results season are given (upper for row) and the wet season (lower row). the dry season (upper row) and the wet season (lower row). of the Amazon basin during the wet season. This is in good (Table 42). These results17523 imply that the Middleman regions agreement with other measures quantifying the contribution are important intermediary regions involved in the alternative 630 of evapotranspiration within cascading moisture recycling 640 pathways to the direct transport of moisture from the Ama- (Figs. 5b and 5d). zon basin to the La Plata basin. In the La Plata basin, the fraction of precipitation that comes from cascading moisture recycling in the Middleman 3.3.2 Betweenness Centrality region is 8% during the wet season and 5% during the dry 635 season. This represents 47% of the fraction of precipitation Cascading moisture recycling pathways are channeled in the that comes from cascading moisture recycling in the conti- south-western part of the Amazon basin and a narrow band nent during the wet season and 35% during the dry season 645 east of the subtropical Andes (Figs. 6b and 6d). Regions with Zemp et al.: Cascading moisture recycling 11 icsinPpr|Dsuso ae icsinPpr|Dsuso ae | Paper Discussion | Paper Discussion | Paper Discussion | Paper Discussion

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case casc (a) εP l (b) εP l (c) ρAm (d) ρAm Title Page Wet season (DJFM) Abstract Introduction

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casc casc (e) εP l (f) εP l (g) ρAm (h) ρAm Full Screen / Esc Fig. 7: Fraction of evapotranspiration which precipitates in the La Plata basin through direct (εP l, a,e) and cascading moisture casc Figurerecycling 7. Fraction (εP l , b,f)of and evapotranspirationfraction of precipitation which which comes from precipitates the Amazon basin over through the direct La (ρAm Plata, c,g) and basin cascading (defined casc casc casc moisture recycling (ρAm , d,h). Considered together, εP l and εP l show source regions of precipitation in the La Plata basin Printer-friendly Version by the red boundaries) through directcasc (εPl, a and e) and cascading moisture recycling (εPl , b (defined by the red boundaries) and ρAm and ρAm show sink regions of evapotranspiration from the La Plata basin (defined and f) andby the redfraction boundaries). of Resultsprecipitation are given for which the dry season comes (JJAS) from (upper therow) and Amazon the wet season (defined (DJFM) (lower by the row). red bound- casc Interactive Discussion aries) basin through direct (ρAm, c and g) and cascading moisture recycling (ρAm , d and h). casc Consideredgionally together, and downwind.ε InPl addition,and ε wePl showedshow that the source east- regionsAppendix Aof precipitation over the La Plata basin casc ern flank of the subtropical Andes - located in the pathway of and ρAm and ρAm show sink regions of evapotranspiration from the La Plata basin. Results are the South American Low Level Jet - plays an important role 760 Moisture recycling ratios given forin the the continental dry season moisture recycling (JJAS) as it(upper channels manyrow) cas- and the wet season (DJFM) (lower row). 755 cading pathways. This study offers new methods to improve A1 Direct moisture recycling ratio our understanding of vegetation and atmosphere feedback17524 on the water cycle needed in a context of land use and climate The fraction of precipitation in grid cell j that comes directly change. from Ω is calculated as: P i∈Ω mij ρΩ,j = , (A1) Pj

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Title Page

Abstract Introduction

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J I Figure B1. Scheme explaining the removal of cascading moisture recycling. (a) Originally, the J I precipitation in the grid cell i (Pi ) is composed by oceanic and continental moisture. The total incoming moisture is evaporated in i (Ei ) and some part of it contributes to precipitation in the Back Close grid cell j (mij ). (b) If we forbid the re-evaporation of continental precipitation, only the precip- Full Screen / Esc itation in i that has oceanic origin (Pi←ocean) is evaporated in i (Ei←ocean) and can contribute to precipitation in j (mij←ocean). By doing so, we remove cascading recycling of continental moisture from the network. Printer-friendly Version

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14 Zemp et al.: Cascading moisture recycling ACPD 14, 17479–17526, 2014

920 in i through cascading moisture recycling: Cascading moisture recycling n−1 D. C. Zemp et al. mit1 Y mtltl+1 mtnj Ci,t1,...,tn,j = · · (C4) Pt Pt Pj 1 l=1 l+1 Title Page

An example of pathway contributions is provided in Fig. C1. Abstract Introduction The contribution of each existing path is calculated between Conclusions References any pair of grid cells in the network. The optimal path is the Tables Figures 925 path with the maximum contribution. J I To ﬁnd the optimal pathway, we use the method J I shortest paths in the package iGraph for Python based Back Close on an algorithm proposed by Newman (2001). In this Figure C1. Diﬀerent cascading moisture recycling pathways from grid cell 1 to grid cell 4. The Fig. C1: Different cascadingW m /P moisture recycling pathways Full Screen / Esc method, the cost of a pathway is calculated as the sum of contribution of the direct pathway is 1,4 = 14 4, the contribution of the path involving one re-evaporationfrom grid cycle cell in grid1 cellto 3 grid is W1,3,4 cell= m134./P The3 · m14 contribution/P 4 and the contribution of the of di- the path 930 the weight of its arrows. In order to adapt the method to involving re-evaporation cycles in grid cells 2 and 3 is W = m /P 2 · m /P 3 · m /P 4. Printer-friendly Version rect pathway is C1,4 = m14/P 4, the1,2,3,4 contribution12 of13 the path14 our purpose, we chose the weight of the arrows as wt t = l l+1 involving one re-evaporation cycle in grid cell 3 is C1,3,4 = Interactive Discussion mt t −log( l l+1 ). The cost of a pathway from grid cell i to grid m /P 3 ∗ m /P 4 and the contribution of the path involv- P 13 14 tl+1 ing re-evaporation cycles in grid cells 2 and 3 is C = cell j as calculated in iGraph becomes: 1,2,3,4 m12/P 2 ∗ m13/P 3 ∗ m14/P 4. 17526 n−1 X C0 = w + w + w i,t1,...,tn,j 1t1 tltl+1 tnj 955 Appendix D l=1 n−1 mit1 X mtltl+1 mtnj Author contribution 935 = −log( ) − log( ) − log( ) Pt Pt Pj 1 l=1 l+1 J.F.D., H.M.J.B., C.-F.S. and D.C.Z. developed the analysis. 1 R.J.E. performed the simulation of WAM-2layers. G.S. pro- = log( m m m ) 1t1 Qn−1 tltl+1 tnj vided the mask of the La Plata basin. D.C.Z. performed the · l=1 ( ) · Pt1 Ptl+1 Pj 960 analysis and prepared the manuscript with contributions from 1 all co-authors. C.-F. S. conceived the project together with = log( ) Ci,t1,...,tn,j J.H. and supervised it together with A.R.

Because the optimal pathway is deﬁned as the pathway with 0 Acknowledgements. This paper was developed within the scope of 940 the minimum cost C , it corresponds to the pathway with the the IRTG 1740 / TRP 2011/50151-0, funded by the DFG / FAPESP. maximum contribution C as deﬁned above. 965 J.F. Donges acknowledges funding from the Stordalen Foundation and BMBF (project GLUES) and R.J. van der Ent from NWO / C2.2 Betweenness centrality ALW. We thank K. Thonicke for comments on the manuscript and P. Manceaux for his help on designing the network schemes. Mathematically, betweenness of the grid cell i is the fraction of the number of optimal pathways between any pair of grid References 945 cells which pass through i:

970 Arraut, J. M. and Satyamurty, P.: Precipitation and Water Vapor Transport in the Southern Hemisphere with Emphasis on the X σjk(i) Bi = (C5) South American Region., J. Appl. Meteorol. Clim., 48, 1902– σjk j,k 1912, 2009. Arraut, J. M., Nobre, C., Barbosa, H. M., Obregon, G., and 975 Marengo, J.: Aerial Rivers and Lakes: Looking at Large-Scale with σjk is the number of optimal pathways between grid cells j and k, and σ (i) is the number of these pathways Moisture Transport and Its Relation to Amazonia and to Subtrop- jk ical Rainfall in South America, J. Climate, 25, 543–556, 2012. that pass through the grid cell i. B reaches values between 0 N−1 2 Bagley, J. E., Desai, A. R., Harding, K. J., Snyder, P. K., and Foley, 950 and 2 = (N − 3N + 2)/2 with N the number of grid J. A.: Drought and Deforestation: Has land cover change inﬂu- cells. To calculate it, we used the directed and weighted ver- 980 enced recent precipitation extremes in the Amazon?, J. Climate, sion of the method betweenness in the package iGraph 27, 345–361, 2014. for Python. The choice of the weights used in this method is Betts, R., Cox, P., Collins, M., Harris, P., Huntingford, C., and explained in Sect. C2.1. Jones, C.: The role of ecosystem-atmosphere interactions in sim-