Green Water
Summary and Keywords
Precipitation falling onto the land surface in terrestrial ecosystems is transformed into either “green water” or “blue water.” Green water is the portion stored in soil and potentially available for uptake by plants, whereas blue water either runs off into streams and rivers or percolates below the rooting zone into a groundwater aquifer. The principal flow of green water is by evapotranspiration from soil into the atmosphere, whereas blue water moves through the channel system at the land surface or through the pore space of an aquifer. Globally, the flow of green water accounts for about twothirds of the global flow of all water, green or blue; thus the global flow of green water, most of which is by transpiration, dominates that of blue water. In fact, the global flow of green water by transpiration equals the flow of all the rivers on Earth into the oceans.
At the global scale, evapotranspiration is measured using a combination of ground, satellite, and modelbased methods implemented over annual or monthly timeperiods. Data are examined for selfconsistency and compliance with water and energybalance constraints. At the catchment scale, average annual evapotranspiration data also must conform to water and energy balance. Application of these two constraints, plus the assumption that evapotranspiration is a homogeneous function of average annual precipitation and the average annual net radiative heat flux from the atmosphere to the land surface, leads to the Budyko model of catchment evapotranspiration. The functional form of this model strongly influences the interrelationship among climate, soil, and vegetation as represented in parametric catchment modeling, a very active area of current research in ecohydrology.
Green water flow leading to transpiration is a complex process, firstly because of the small spatial scale involved, which requires indirect visualization techniques, and secondly because the nearroot soil environment, the rhizosphere, is habitat for the soil microbiome, an extraordinarily diverse collection of microbial organisms that influence water uptake through their symbiotic relationship with plant roots. In particular, microbial polysaccharides endow rhizosphere soil with properties that enhance water uptake by plants under drying stress. These properties differ substantially from those of nonrhizosphere soil and are difficult to quantify in soil water flow models. Nonetheless, current modeling efforts based on the Richards equation for water flow in an unsaturated soil can successfully capture the essential features of green water flow in the rhizosphere, as observed using visualization techniques.
There is also the yetunsolved problem of upscaling rhizosphere properties from the small scale typically observed using visualization techniques to that of the rooting zone, where the Richards equation applies; then upscaling from the rooting zone to the catchment scale, where the Budyko model, based only on water and energybalance laws, applies, but still lacks a clear connection to current soil evaporation models; and finally, upscaling from the catchment to the global scale. This transitioning across a very broad range of spatial scales, millimeters to kilometers, remains as one of the outstanding grand challenges in green water ecohydrology.
Keywords: ecohydrology, soil water, evapotranspiration, Budyko model, Richards equation, transpiration, water cycle, rhizosphere
Introduction
Green water is the water accumulating in soil after the infiltration of rainfall (Falkenmark & Rockström, 2006; Rockström et al., 2014). Thus it is soil water potentially available for uptake by plant roots and subsurface biota, because it did not run off into streams and rivers or percolate below the rooting zone into an aquifer to replenish groundwater. The portion of incoming precipitation that does not become green water is termed blue water (Falkenmark & Rockström, 2006; Rockström et al., 2014). Thus blue water refers to the water flowing in streams and rivers, stored in lakes and reservoirs, or pumped from groundwater. It is the water used by humanity for drinking, bathing, cooling, and pollutant disposal, the water humanity must share with all other forms of life, who use it for the same purposes.
Aside from infiltration into and redistribution within soil, the flow of green water is either by transpiration—water movement into plant roots, then upward in the plant to exit through its leaves—or by evaporation directly from the land surface, both pathways returning green water to the atmosphere as water vapor. Thus green water moves from soil pores into the atmosphere, whereas blue water moves through channels at the land surface or through the pore space in an aquifer below the land surface. As will be shown in the following section, the global flow of green water accounts for about twothirds of the total global flow of any water, green or blue (Rodell et al., 2015). There are also virtual flows of both green and blue water, defined as the water used to produce commodities traded among nations. Green water accounts for 85%–88% of these virtual flows (Konar, Dalin, Hanasaki, Rinaldo, & RodríguezIturbe, 2012; Hoekstra & Mekonnen, 2012), which are increasingly subject to competition among nations (Suweis, Rinaldo, Maritan, & D’Odorico, 2013). Thus, the global flow of green water, whether actual or virtual, dominates that of blue water.
Despite the longrecognized global dominance of green water flow, its hydrologic behavior has been investigated at the same level of detail as blue water only after the year 2000 (Rockström & Falkenmark, 2000). The present article is therefore intended as an introduction to the hydrology of green water at global, catchment, and point site scales, with the point site focus being on the rhizosphere, the portion of a soil ecosystem that is significantly influenced by plant roots, the agents of green water flow by transpiration. The state of current knowledge about green water dynamics is reviewed at the three spatial scales indicated, and key areas where this knowledge is in greatest need of improvement are identified. As will become evident in what follows, the grand challenge for hydrologic research is to understand the fundaments of green water availability and productive flow in terrestrial ecosystems as the basis for management strategies that are comparable in scope and sophistication to those already in place for blue water.
Green Water at the Global Scale
The principal flow of green water, aside from infiltration into and redistribution within the rooting zone of soils, is by evapotranspiration (ET), defined in the present context as the transfer of water from a vegetation canopy, the land surface, or surface freshwater into the atmosphere. This transfer of water is highly variable, both spatially and temporally, and is challenging to measure directly, even at a single location. Therefore, indirect measurement using combinations of groundbased, satellitebased, and modelbased methods is the current preferred approach to determining ET at continental to global scales, over either annual or monthly time periods (Rodell et al., 2015). Data from multiple sources of comparable quality are typically averaged and then optimized by subjecting them to the constraints of selfconsistency (e.g., the mean annual value must equal the sum of mean monthly values) and water balance (precipitation less runoff equals ET, change in storage being neglected at continental to global scales), as well as energy balance, since latent heat flux, the transfer of energy associated with ET from the Earth’s surface to the atmosphere, and ET are equivalent processes. This selfconsistent methodology and its current status are reviewed and illustrated in detail by Rodell et al. (2015).
Table 1 lists optimized values of the mean annual global terrestrial precipitation, ET, and runoff from the continents into the oceans pertaining to the global water cycle as it occurred during the first decade of the current millennium (Rodell et al., 2015). Globally, the mean annual flow of green water to the atmosphere is seen to be about 54% larger than the mean annual flow of blue water out of the continents. Table 2 shows this kind of comparison made for the continents individually. With the notable (and minor) exception of Antarctica, predominance of green water flows to the atmosphere over blue water flows to the ocean occurs also at continental scales, with the relative differences between the former and the latter ranging from 10% (Australasia) to 142% (Africa).
Table 1. Global values (10^{3} km^{3} yr^{−1}) of mean annual terrestrial precipitation, evapotranspiration, and runoff into the oceans.
Component 
Global Flow 

Precipitation 
116.5 ± 5.1 
Evapotranspiration 
70.6 ± 5.0 
Runoff into Oceans 
45.9 ± 4.4 
Source: Rodell et al. (2015).
Table 2. Optimized mean annual flows (10^{3} km^{3} yr^{−1}) of green water (ET) and blue water (runoff) out of the continents.
Continent 
Green 
Blue 

Africa 
16.8 
3.8 
Antarctica 
0.1 
2.3 
4.0 
3.6 

Eurasia 
22.5 
16.0 
North America* 
9.9 
7.9 
South America 
17.3 
12.3 
Notes: (*) includes Australia, Indonesia, and the islands of Australasia;
(**) includes Greenland.
Source: Rodell et al. (2015).
Evapotranspiration is the sum of abiotic evaporation from the land surface, vegetation canopies, and freshwater bodies, plus transpiration (T) from plants after the uptake of green water into their roots, subsequent movement through the plant conductance system, and finally exit through leaf stomata. Transpiration, especially in an agricultural context, is also termed productive green water flow (Rockström & Falkenmark, 2000), because it is the only ET mode directly supporting carbon assimilation and primary productivity. The quantitative partitioning of ET into evaporation and transpiration is therefore an important and abiding area of ecohydrology research which remains challenging because of the difficulties in measuring ET directly (Rodell et al., 2015; Zhou, Yu, Zhang, Huang, & Wang, 2016).
Schlesinger and Jasechko (2014) have surveyed the recent literature to compile values of the ratio T/ET for nine terrestrial biomes (Table 3). These values, determined by groundbased measurements of green water flow, sap flow, or oxygen isotope composition differences between green water and blue water near the land surface, show a tendency to be larger in wetter climates.
Table 3. Global transpiration data for terrestrial biomes.
Biome 
T/ET (%) 

Tropical Rainforest 
70 ± 14 
Tropical Grassland 
62 ± 19 
Temperate Deciduous Forest 
67 ± 14 
Temperate Coniferous Forest 
55 ± 15 
Boreal Forest 
65 ± 18 
Temperate Grassland 
57 ± 19 
Steppe 
48 ± 12 
Mediterranean Shrubland 
47 ± 10 
Desert 
54 ± 18 
Source: Schlesinger and Jasechko (2014).
The average global T/ET, calculated as the sum of the biome T/ET values weighted according to either the volume of precipitation into or the volume of ET out of a given biome, was reported as 61 ± 15%. This figure is in good agreement with recent estimates of global T/ET for both natural biomes and croplands as assessed by a variety of ground and modelbased methods (Evaristo, Jasechko, & McDonnell, 2015; Good, Noone, & Bowen, 2015 Zhou et al., 2016; Maxwell & Condon, 2016; Berkelhammer et al., 2016), thus indicating clearly that T is the larger component of terrestrial ET. Using the average global T/ET estimate and the ET value listed in Table 1, one calculates, remarkably, that the volume of global green water flow by transpiration is approximately equal to the volume of global blue water flow by runoff. Thus, the annual flow of green water through plant roots into the atmosphere matches the annual flow of all the rivers in the world to the oceans.
Agricultural biomes (croplands and pasturelands) currently occupy about 38% of the icefree land surface on Earth (Foley et al., 2011) and account for about 25%–30% of the global ET (Rost et al., 2008). The total annual green water flow from croplands is estimated to be about 7,000 km^{3} yr^{−1} (Rost et al., 2008; Mekonnen & Hoekstra, 2011), with a similar magnitude of green water flow occurring from pasturelands (Rost et al., 2008). Values of T/ET for cropland biomes, when they are wellmanaged, are comparable to the global average T/ET given above (Zhou et al., 2016), but much lower values of cropland T/ET occur in developing countries, with correspondingly low crop yields (Sposito, 2013).
Green water flow from pasturelands is a similar process to that from natural biomes, but green water flow from croplands is derived in part from the conversion of blue water, applied to croplands through irrigation, into green water once it infiltrates into soil. Mekonnen and Hoekstra (2011) estimate that 10%–15% of the global green water flow from croplands originates in this way (i.e., almost all croplands are rainfed, not irrigated). This conversion of blue water to green water is termed a consumptive use of blue water: blue water that is withdrawn, used, and subsequently evaporated into the atmosphere without being returned to the blue water flow system. Consumptive blue water use is also termed the blue water footprint (Mekonnen & Hoekstra, 2011; Hoekstra & Mekonnen, 2012). Hoekstra and Mekonnen (2012) estimated the combined global water footprint of agricultural production, industrial production, and domestic water supply for the period 1996–2005 to be about 9,100 km^{3} yr^{−1}, 92% of which was attributed to agricultural production.
Green Water at the Catchment Scale
A catchment is a terrestrial ecosystem whose spatial domain is defined by the area drained by a river and its tributaries. When averaged over several decades, the annual flow of green water from a catchment into the atmosphere is subject to the same water and energy balance assumptions as is the global flow of green water (Rodell et al., 2015), that is, negligible changes in subsurface water storage and negligible net heat transfer between the land surface and subsurface zones (Arora, 2002). Given these two assumptions, the longterm average annual water and energy balance at the catchment scale can be expressed mathematically in the form (Budyko, 1974; Arora, 2002):
and
where P represents the average annual precipitation, Q is average annual runoff, R_{n} is the average annual net radiative heat flux from the atmosphere to the land surface, L is the latent heat of evaporation (the energy per unit volume required to transform a liquid or a solid into a gas), the product L ET then being the latent heat flux, and H is the average annual heat flow from the land surface into the atmosphere, termed the sensible heat flux. Equation (1) states that the precipitation falling onto a catchment is not stored and so must leave as a flow of either green water (ET) or blue water (Q). Equation (2) states that the solar radiation impinging onto a catchment is not stored beneath the land surface and so must leave, either as heat carried off by green water flow (L ET) or as radiation from the land surface back into the atmosphere (H). The units of the quantities in Eq. (1) are those of volume per unit area of land surface per year, while the units of the quantities in Eq. (2) are those of energy per unit area of land surface per year.
Equation (1) is quantified by combining hydrological, climatological, and ecological data taken at the catchment scale over at least five decades [see, e.g., Ye et al., 2015, for a discussion of current methodologies]. As noted in the previous section, ET and latent heat flux are equivalent processes that link Eq. (1) with Eq. (2), which fact suggests dividing Eq. (2) on both sides by L to give it the same units as Eq. (1):
Equation (3) can be interpreted physically as an energybalance constraint imposed on ET analogous to the waterbalance constraint imposed on ET by Eq. (1). Evidently the maximum ET occurs when all incoming radiation energy is consumed by the evaporation of water from the land surface and there is negligible sensible heat flux. According to Eq. (3), this maximum ET must equal R_{n}/L, which then may be designated ET_{0} and termed the potential evapotranspiration (Budyko, 1974). Potential evapotranspiration is achieved when the incoming radiation is relatively weak and the amount of green water available for ET is not limiting (Budyko, 1974; Arora, 2002).
Budyko (1974), in a nowclassic synthesis of climatological and hydrological data on catchments, hypothesized that Eq. (1) and (3) imply that there exists a functional relationship among ET, P, and ET_{0} which applies to all catchments:
He further concluded on the basis of available data that Eq. (4) is subject to two limiting conditions:
Equation (5a) describes a “wet condition” of high available green water and low sensible heat flux, whereas Eq. (5b) describes a “dry condition” of low available green water and high sensible heat flux. Under the wet condition, ET is energylimited, whereas under the dry condition ET is waterlimited. Runoff is high under the wet condition, low under the dry condition.
The Budyko hypothesis, Eq. (4), can be developed further mathematically after making the assumption that F(ET_{0}, P) is a homogeneous function of its arguments (see, e.g., Hankey & Stanley, 1971). Homogeneity means that, if the variables ET_{0}, P are each scaled by a factor λ, the value of F(ET_{0}, P) is also scaled by the factor λ:
Equation (6) is, in fact, implicit in the Budyko hypothesis, given that it stipulates Eq. (4) should apply to all catchments, which accordingly are being viewed as scaled versions of one another in respect to evapotranspiration and precipitation. Hankey and Stanley (1971) proved that the property of homogeneity as expressed in Eq. (6) is mathematically equivalent to the functional representation:
which Hankey and Stanley (1971) show is equally valid as an alternative to Eq. (6) for defining a homogeneous function of ET_{0} and P. Equation (7) is in fact the form of Eq. (4) originally presented by Budyko (1974). The ratio ET_{0}/P is termed the aridity index and given the symbol φ (Arora, 2002). Values of φ < 1 conventionally indicate a humid climate, whereas φ > 1 indicates an arid climate. The limiting conditions on Eq. (7) that follow from Eq. (5) are (Zhou, Yu, Huang, & Wang, 2015):
It follows from Eq. (8) that a plot of Eq. (7) emanates from the origin as a curve tangent to the line, ET/P = ET_{0}/P, then turns concave to the xaxis and asymptotically approaches a horizontal line defined by ET/P = 1.
Budyko (1974) tested Eq. (7) successfully using water and energy balance data for more than 1,000 catchments encompassing a variety of biomes, showing also that the limiting conditions in Eq. (8) were met. Over the ensuing four decades, a large number of successful tests of Eq. (7) have been reported, based on compiled experimental measurements (Jones et al., 2012; Wang & Yang, 2014; Ye et al., 2015) or model simulations (Koster & Suarez, 1999; Arora, 2002). A test of Eq. (7) using experimental measurements is shown in Figure 1, based on data collected daily for 50 years (1951–2000) for more than 250 catchments in the United States that span a variety of climatic zones and physiographic regions (Ye et al., 2015).
As noted by Arora (2002), although scatter in plots of data according to Eq. (7) is always apparent, these successful tests demonstrate “the primary control of precipitation and available energy in determining the ratio of annual evapotranspiration to precipitation.” Accordingly, a plot of catchment data according to Eq. (7) is termed a “Budyko plot.” Because of the longterm balance conditions assumed in Eq. (1) and (2), data conforming to Eq. (7) should not appear above the dashed line in Figure 1 that emanates from the origin or above the horizontal dashed line in the figure defined by ET/P = 1. Individual data points, however, may violate one of these constraints (an example occurs in Figure 1), which implies an inadequacy of either the data plotted or the assumptions made about subsurface storage leading to the longterm water and energybalance conditions expressed by Eq. (1) and (2), respectively.
Wang, Wang, Fu, and Zhang (2016) have presented a comprehensive review of the Budyko hypothesis, including recent studies that model data scatter not caused by inaccurate measurements, evidently reflecting specific catchment characteristics, as well as studies that incorporate mechanistic ecohydrological processes into the Budyko framework or extend it to smaller temporal and spatial scales than those to which Eq. (1) and (2) are applicable (e.g., Biswal, 2016). In respect to these latter issues, Gentine, D’Odorico, Lintner, Sivandran & Salvucci (2012) have cautioned that data scatter is an expected artifact if annual catchment data are used to test Eq. (7) and (8) instead of longterm average annual data. They also note that the Budyko framework provides a strong constraint on the interrelationship among climate, soil, and vegetation as represented in parametric catchment models. This constraint can be put into quantitative form if an explicit mathematical expression is available for Eq. (7). Budyko (1974) proposed an interpolation formula based on Eq. (8) which has been widely used, but a variety of nonparametric and oneparameter models of Eq. (7) also have been proposed during the past 40 years (Zhou et al., 2015).
Zhou et al. (2015) discussed parametric Budyko models in the context of a general approach that takes advantage of the fact that ET in Eq. (4) is a homogeneous function of ET_{0} and P as defined by Eq. (6). Any such function must obey the wellknown Euler Relation (see, e.g., Callen, 1985):
It follows by a straightforward rearrangement of Eq. (9) that:
where
and
are termed, respectively, the partial elasticities of ET with respect to P and ET_{0}. The partial elasticity m_{p} provides a quantitative measure of the relative change in ET with respect to a relative change in P at fixed ET_{0}, whereas the partial elasticity m_{et} provides a quantitative measure of the relative change in ET with respect to a relative change in ET_{0} at fixed P. Since both partial derivatives in Eq. (9) are positivevalued, both partial elasticities are positivevalued, and they are constrained as shown in Eq. (10).
Zhou et al. (2015) showed that postulating the functional dependence of the ratio, m_{p}/m_{et}, on the aridity index φ is sufficient, along with the constraint imposed in Eq. (10), to derive an explicit mathematical form for F(φ) on the right side of Eq. (7). In particular, if the ratio is set equal to a simple power of φ, say φ^{n} (n > 0), then it follows that:
which Zhou et al. (2015) show to be a generic oneparameter model encompassing several previously proposed explicit mathematical forms for F(φ). Equations (7) and (12) define what may be termed a “Budyko curve.” Evidently the model parameter n should depend to some extent on the ecohydrological properties of a catchment. For example, Donohue, Roderick, and McVicar (2012) and Yang, Donohue, and McVicar (2016) correlate n with green water characteristics of a catchment, such as the depth of the rooting zone. Zhang, Yang, Yang, and Jayawardena (2016) have shown that n can also be correlated with the vegetation characteristics of river basins in China. Roderick and Farquhar (2011) have given a broad ecohydrological discussion of the catchment properties, including disturbances, which could influence the value of n in Eq. (12). No physical basis has been established thus far, however, for the particular choice of a powerlaw expression to represent the partial elasticity ratio, m_{p}/m_{et}. Denoting this ratio by g(φ), Zhou et al. (2015) show quite generally that the analogs of Eq. (8) are:
Thus 0 < g(φ) < ∞ and, like F(φ), it has a positive first derivative with respect to φ. A powerlaw model of g(φ) is not necessary in order to derive an expression for F(φ) that satisfies Eqs. (4) to (11). Any smooth, monotonicallyincreasing, positive function of φ which satisfies Eq. (13) is a candidate for expressing g(φ) mathematically.
Green Water in the Rhizosphere
The rhizosphere (Figure 2) is the portion of a soil ecosystem affected significantly by the presence of plant roots (Bengough, 2012; Oburger & Schmidt, 2016). Although the rhizosphere around any one root is a layer of soil less than 5 mm thick next to the root surface (in the present context, termed the rhizoplane), all transpired water has to pass through this very tiny zone, leading, remarkably, to a flow of green water that globally matches the flow of all the rivers on the planet into the oceans. The rhizosphere ecosystem through which green water travels is extraordinarily biodiverse, being highly enriched in the bacteria, fungi, archaea, and microfauna constituting the soil microbiome, the result of plant roots having evolved a mutualistic relationship with their vicinal microbes (Berendsen, Pieterse, & Bakker, 2012; Nielsen, Wall, & Six, 2015; Berg, Rybakova, Grube, & Köberl, 2016). This symbiotic relationship is driven by root exudation of compounds beneficial to the microbiome (Figure 3), which in turn responds by catalyzing nutrient cycling essential for plant growth and fitness, assisting plants in resisting pathogens and helping them to promote resilience under environmental stress (Berendsen et al., 2012; Haney & Ausubel, 2015; Berg et al., 2016; Carey, 2016). Understanding the structure and functioning of the rhizosphere ecosystem has thus emerged as a major theme in current research on plantsoil interactions (Nielsen et al., 2015; van der Heijden & Schlaeppi, 2015; Berg et al., 2016; Carey, 2016).
Given the importance of root exudates in the functioning of the rhizosphere, much attention has been given to the development of techniques for sampling rhizosphere soil solutions to measure their chemical compositions. These techniques, operational compromises between chemical accuracy and analytical convenience, include highspatialresolution (microliter to milliliter samples) in situ methods involving microsuction cups or microdialysis (Berg et al., 2016). The result is either a resident composition, obtained by removing a rhizosphere soil solution sample “instantaneously” (microsuction cups), or a flux composition, obtained by allowing “natural” rhizosphere soil solution flow into a collector (microdialysis). The accuracy of these techniques is of course influenced by whatever disturbance of the rhizosphere has occurred because of its interaction with the apparatus employed. If for no other reason than differences in the region of rhizosphere pore space sampled, a flux composition will usually differ from a resident composition of a rhizosphere soil solution.
Perhaps of most relevance to the flow of green water in the rhizosphere is the current effort to develop accurate techniques for the in situ imaging of rhizosphere structure and function. In the case of green water, the ultimate goal of this effort is the development of mathematical models of rootinduced water movement based on highresolution images of rhizosphere architecture at micrometer to decimeter spatial scales, over time scales ranging from seconds to months (Roose et al., 2016). The principal imaging techniques applied are Xray computed tomography (Beckers et al., 2014; Daly et al., 2015), neutron computed tomography or radiography (Moradi et al., 2011; Zarebanadkouki, Kroener, Kaestner, & Carminati, 2014; RudolphMohr, Vontobel, & Oswald, 2014), and magnetic resonance imaging (Oswald et al., 2015). Applications of these techniques, reviewed comprehensively by Roose et al. (2016), include visualization of changes in rhizosphere soil structure, porosity, and water content as caused by either roots or the rhizosphere microbiome. Roose et al. (2016) discuss a dozen challenges for the future development of rhizosphere visualization techniques, among them direct imaging the flow of green water leading to transpiration. Neutron radiography has proven especially useful for this purpose, as illustrated in Figure 4, which shows that distinct differences in water content occur in the rhizosphere depending on whether it contacts older or younger portions of a root (Roose et al., 2016), the older portions being the more effective in water uptake (Carminati, 2013).
From a biophysical perspective, the most important plant root exudate affecting the flow of green water by transpiration is mucilage, a complex mixture of organic compounds comprising mainly polysaccharides with some lipids (Carminati, Zarebanadkouki, Kroener, Ahmed, & Holz, 2016). Like other organic root exudates, mucilage is accessed as a carbon source by the rhizosphere microbiome, but it is also admixed with microbial polysaccharide exudates to form what is termed mucigel (Figure 2). Reviewing previous studies of the role of mucigel, Carminati (2012) proposed that mucigel in rhizosphere soil swells to many times its original volume when it is wet and, doing so, endows the rhizosphere with a higher green water availability than would occur at the same water potential in nonrhizosphere soil, thereby enhancing the ability of plants to take up green water and resist drought stress in a drying soil. Ahmed, Kroener, Holz, Zarebanadkouki, and Carminati (2014) gave a proofofprinciple demonstration of this hypothesis through experiments in which mucilage extracted from chia seeds was mixed into a sandy soil whose water retention curve was determined and compared to that for the same soil without added mucilage. Their results showed that, at any water potential, the water content of the soil to which mucilage had been added was indeed always higher than that of the soil without mucilage. Ahmed et al. (2014) also found that the soil mixed with mucilage dried much more slowly than the soil without mucilage added. Carminati et al. (2016) then gave a proofofprinciple calculation of the expected green water availability increase from the soil concentration of mucilage used in the experiments of Ahmed et al. (2014), showing that the computed increase is comparable to the typical increase observed experimentally. Carminati et al. (2016) concluded their analysis by proposing three issues for future research: (a) the effect of mucigel on the rhizosphere soil hydraulic conductivity, (b) the distribution of mucigel in the pore space of rhizosphere soil, and (c) the spatial variation of the water potential near roots in a drying soil under varying transpiration demand. In their view, combining quantitative measurements with highresolution imaging is the key to unraveling the mechanisms of green water flow into plant roots.
The mathematical modeling of green water flow in the rhizosphere leading to transpiration is based on the Richards equation, a partial differential equation that describes water movement through an unsaturated soil (Warrick, 2003; Schwartz, Carminati, & Javaux, 2016):
where $\nabla $ is the gradient operator in threedimensional space, θ is volumetric water content at a point in the rhizosphere, K is hydraulic conductivity at the same point, h is water potential, z is the vertical coordinate, and S is the rate at which water enters the roots because of transpiration demand. In Eq. (14), the left side is the change in volumetric water content with time at a given point within a small volume of rhizosphere soil, while the right side is the net rate of water accumulation in this small volume as caused by gradients in water potential (h) and gravitational potential energy (z), minus the rate of water loss from the small volume caused by root uptake under transpiration demand (S). Thus Eq. (14) is a statement of mass balance for green water in a small volume of rhizosphere soil. It is also a nonlinear partial differential equation because K, h, and S all depend on θ. The mechanistic basis of the Richards equation derives from a continuum approach to multiphase flows in porous media that invokes linear flux relationships that, in the present context, feature three empirical parameters, K, h, and S, whose functional dependence on volumetric water content is presumed known from experiment (Warrick, 2003). Explicit mathematical models of these three parameters as functions of θ are presented by Schwartz et al. (2016). More generally, Assouline and Or (2013) have reviewed the buffet of mathematical models available for expressing the dependence of soil hydraulic properties on the volumetric water content, including a discussion of their conceptual foundations and experimental validation.
In a given small volume of rhizosphere soil, the volumetric water content may be partitioned as the weighted average of the water content in pores not containing mucigel (θ_{b}), which are therefore like those in nonrhizosphere soil, plus that in pores containing mucigel (θ_{m}), with the weighting factor being chosen as the fraction of pores not containing mucigel (Kroener, Zarebanadkouki, Kaestner, & Carminati, 2014). Moreover, at least in principle, the water content in the pores containing mucigel is influenced by the timevariation of the response of mucigel itself to changing water potential (e.g., a decreasing mucilage volume in response to decreasing water potential during drying), such that Eq. (14) must be augmented by a “relaxation model” describing the changes in θ_{m} with time caused by a noninstantaneous mucigel response to changing water potential, as discussed in detail by Kroener et al. (2014). This model can be introduced into the left side of Eq. (14) after expressing θ as the weighted average of θ_{b} and θ_{m} (Kroener et al., 2014; Schwartz et al., 2016). Schwartz et al. (2016) have solved the Richards equation numerically to simulate a sandy rhizosphere soil drying under a constant transpiration demand after introducing conventional models of the θdependence of the three dependent variables on the right side, as well as the “relaxation model” of Kroener et al. (2014) for the effect of finite mucigel response time on the timevariation of θ_{m} along with their model for the enhancing effect of mucigel on the hydraulic conductivity at a given water content. Some typical results of the numerical calculations by Schwartz et al. (2016) are shown in Figure 5, which presents the water content distribution near a root as seen in a vertical cross section (xz plane) after the soil has been subjected to transpiration demand for the four elapsed times (in days) labeled across the top of the figure. The x and zaxes of each cross section are marked in units of centimeters, with the vertical datum being the top of the soil and the horizontal datum being the position of the root, which is 5 cm long and 1 mm wide. The bottom row of cross sections represents nonrhizosphere soil (Control) for comparative purposes (i.e., θ_{m} = 0 and no effect of mucigel on K), while the middle row represents rhizosphere soil with no “relaxation effect” (Static) and the top row (Dynamic) represents rhizosphere soil with the “relaxation effect” included.
For both the Static and Dynamic scenarios, the water content around the root is consistently higher over time than it is for the Control scenario. For example, after 10 days, the average water content in the Static scenario is 68% higher than in the Control scenario, and that in the Dynamic scenario is 127% higher than in the Control scenario. Consistent with this result, the actual transpiration rate, as determined by the calculated water uptake into the root under a constant transpiration demand, began to decrease from its potential value at a later time under the Static and Dynamic scenarios than it did under the Control scenario. These simulation results also are consistent with neutron radiography imaging studies showing higher water content in rhizosphere soil than in nonrhizosphere soil (Schwartz et al., 2016). Thus, according to the model of Schwartz et al. (2016), mucigel in the rhizosphere should reduce water stress caused by soil drying under transpiration demand.
Kroener, Zarebanadkouki, Bittelli, and Carminati (2016) have also solved the Richards equation incorporating a relaxation model to simulate root water uptake under transpiration demand (Kroener et al., 2014). Their numerical simulations for rhizospheres with and without mucilage were compared directly to available experimental data on transpiration by wheat plants. In all cases, the simulations of a rhizosphere with mucilage gave a much better fit to the data than those of a rhizosphere without mucilage. The good agreement led Kroener et al. (2016) to conclude that “mucilage softens drought stress in plants.” Further validation of this conclusion is a primary goal of research on rhizosphere visualization and numerical modeling, as noted in the reviews by Roose et al. (2016) and Carminati et al. (2016).
Conclusions and Future Prospects
Green water is the water entering soils from precipitation (and, in some locales, through irrigation) which is not lost to subsurface runoff or deep percolation and, therefore, is stored in the rooting zone, potentially available for plant uptake. Its return to the atmosphere as evapotranspiration globally accounts for almost twothirds of the fate of all precipitation falling onto terrestrial ecosystems (Table 1), with almost twothirds of this return flow being water transpired by plants (Table 3). The global volume of transpiration flow alone is at least as large as the runoff of all rivers into the oceans. Despite this fact, green water has been far less researched than blue water.
Although green water flow as evapotranspiration from agricultural land (inclusive of both cropland and pastureland) makes up only 30% of the global ET coming from terrestrial ecosystems, green water, not blue water, accounts for nearly all of the consumptive use of water in agricultural production, and agricultural products themselves account for 92% of all the water consumed by humanity (Rost et al., 2008; Mekonnen & Hoekstra, 2011; Hoekstra & Mekonnen, 2012). These remarkable statistics underscore the urgent need to understand the ecohydrology of green water in detail as the basis for green water management strategies in agriculture that match in their level of sophistication those already developed for the blue water used in irrigation (Sposito, 2013; Rockström et al., 2014), which globally accounts for less than 10% of the water consumed in agricultural production.
A similar need for improved understanding in respect to green water and its flow as ET exists at the catchment scale, where a close coupling exists between green water and both surface and subsurface blue water in the Critical Zone, a spatial domain extending from the top of the vegetation canopy to the bottom of the groundwater aquifer in a terrestrial ecosystem (Brooks et al., 2015). In the Critical Zone, coupling with ET necessarily includes the vegetation canopy, which can be strongly affected by land use change (Gerten, 2013). The Budyko model [Eq. (7)], with its incorporation of steadystate water and energy balance [Eqs (1) and (2)], provides a suitable framework within which to investigate ETvegetation coupling (Gentine et al., 2012), as exemplified by a recent study of the effect of deforestation on wetlands ecosystem hydrology (Woodward, Shulmeister, Larsen, Jacobsen, & Zawadski, 2014). Applying a parametric version of the Budyko model, Woodward et al. (2014) estimated the effect of deforestation, which decimates T, on reducing wetlands ET and, therefore, increasing wetlands Q [defined in Eq. (1)]. They found that this effect was maximal (ca. 15% increase in Q/P, sufficient to convert swamps into lakes) at φ = 1, the critical value of the aridity index separating humid from arid climates. This example nicely illustrates how the Budyko model of average annual green water flow at the catchment scale constrains the interdependence among vegetation, soil, and climate in the Critical Zone (Gentine et al., 2012).
The Budyko model [Eq. (7)] may be understood as the result of imposing the condition on the Budyko hypothesis [Eq. (4)] that ET is a homogenous function of P and ET_{0} [Eq. (6)], which implies that catchments with widely differing values of ET and the climate variables on which it depends are simply scaled versions of one another, such that ET/P and ET_{0}/P for all catchments will lie on a single “master curve,” as suggested by Figure 1. However, despite a long history of research (see, e.g., Eagleson, 1978), the Budyko model still lacks the fundamental connection to green water dynamics at fieldtocatchment scales that would allow a facile ecohydrological interpretation of its parameters [e.g., Eq. (12)] to give it a basis in the physics of soil evaporation processes (Or, Lehmann, Shahraeeni, & Shokri, 2013; Gentine et al., 2012 Ciocca, Lunati, & Parlange, 2014; Wang et al., 2016; Sprenger, Leistert, Gimbel, & Weller, 2016).
On the other hand, this kind of fundamental connection has been made for green water flow in the rhizosphere leading to transpiration, which is modeled mathematically with the wellknown Richards equation [Eq. (14)] describing water flow in unsaturated soils (Sposito, 1995; Warrick, 2003; Carminati, 2012, de Willigen et al., 2012). At the very small spatial scale of the rhizosphere, direct observation of green water flow is made possible using visualization software that interprets Xray, neutron, or microwave absorption data to create threedimensional images (Roose et al., 2016). These images successfully guide application of the Richards equation, but significant complications enter because the rhizosphere is also a habitat for the soil microbiome, which greatly influences plant uptake of both nutrients and water (Oburger & Schmidt, 2016).
In particular, green water flow in the rhizosphere is affected strongly by the presence of the microbial polysaccharide product, mucigel (Figure 2), whose hydrophilic nature appears to increase green water availability to plants in a drying soil as a strategy to resist drought stress. Although this process has been modeled successfully (Figure 5), a number of issues remain unresolved, particularly the spatial distribution of mucigel in the rhizosphere and the measurement of rhizosphere hydraulic properties (Carminati et al., 2016). To this list may be added the very complex problem of “upscaling” rhizosphere properties from the small spatial scales typically observed using visualization techniques to that of the rooting zone, which is the last and perhaps most difficult of the dozen challenges thrown out by Roose et al. (2016) in their review of imagebased modeling of rhizosphere processes. This challenge does not stop at the scale of the rooting zone, but extends from that scale to the catchment scale, where the Budyko model, based only on water and energybalance laws, still lacks a clear connection to green water dynamics through the Richards equation (Or et al., 2013; Sprenger et al., 2016), and finally from the catchment scale to the global scale, an issue discussed in the review by Rodell et al. (2015). Upscaling of the Richards equation across this very broad range of spatial scales remains as one of the outstanding challenges in green water ecohydrology.
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