research report How much water does a woodland or plantation use: a review of some measurement methods

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1 research report knowledge for managing Australian landscapes How much water does a woodland or plantation use: a review of some measurement methods Rhys Whitley and Derek Eamus University of Technology Sydney Number 6 in a series of 6 1

2 About the authors Rhys Whitley Rhys Whitley is a final year PhD student at the University of Technology, Sydney. His project involves modeling water and carbon fluxes from and to tree canopies. He has developed a modified Jarvis- Stewart model which allows estimation of rates of tree water use from widely available and simple meteorological data and three simple parameters (atmospheric and soil water content and net radiation levels). Derek Eamus Derek Eamus is Professor of Environmental Sciences at the University of Technology, Sydney. A Land & Water Australia senior research fellow, he specialises in the study of the ecohydrology of Australian landscapes, including the measurement and modeling of landscape water and carbon fluxes, the influence of climate change on forests and the function of groundwater dependent ecosystems. Published by: Land & Water Australia, June 2009 Product Code: IDPN30133 Print ISBN: Electronic ISBN: Postal address: GPO Box 2182, Canberra ACT 2601 Office Location: Level 1, The Phoenix Northbourne Ave, Braddon ACT Telephone: Facsimile: Land&WaterAustralia@lwa.gov.au Internet: lwa.gov.au Disclaimer The information contained in this publication is intended for general use, to assist public knowledge and discussion and to help improve the sustainable management of land, water and vegetation. To the extent permitted by law, the Commonwealth of Australia, Land & Water Australia (including its employees and consultants) the authors, and its partners do not assume liability of any kind whatsoever resulting from any person s use or reliance upon the content of this publication. For further information contact Derek Eamus, Professor of Environmetnal Sciences, University of Technology, Sydney PO Box 123, Broadway, NSW

3 Key points Determining the water balance of a landscape is important to sustainable management of water, vegetation and land resources. Water flow through vegetation is the principle pathway for the discharge of water from Australian landscapes. The rate of this discharge is determined by solar radiation, leaf area index, vapour pressure deficit and soil moisture content. Tree transpiration from plantations and native woodlands and forests is an important determinant of the water balance of much of the Australian landscape. Several contrasting methods of measuring and modelling rates of transpiration from vegetation are reviewed, including the Penman-Monteith equation and the Jarvis- Stewart approach. The conceptual frameworks and application of the Budyko, Choudhury and Zhang methods and application of remotely sensed methods are also discussed. Several field-based methods of measuring tree and landscape water use, including sapflow techniques, eddy covariance and scintillometery are briefly discussed. Riparian vegetation is generally a larger user of water than vegetation situated much further away from the river. Woodland and plantation water use Site water balance The water balance of a site provides the framework for studying the ecohydrological behaviour of that site. Understanding the water balance is required for any assessment of how changes in catchment conditions (eg., land use change or climate change) can alter the partitioning of rainfall into different components (for example, evapotranspiration, water yield and groundwater recharge). A site s water balance can be viewed as a model of soil moisture dynamics forced by a semi random climate; or to put it more simply, a bucket. Water enters the bucket as precipitation and leaves the bucket as evapotranspiration, runoff or groundwater recharge. The soil column of a site continuously responds to events of precipitation and to the processes of evapotranspiration, runoff and deep drainage (groundwater recharge). Water is accepted by the soil during periods of precipitation and this storage of water may be: removed from the soil profile through evaporation taken up by vegetation through transpiration drain to the water table, or lost as surface runoff. The water balance for a catchment can be written as: P = E + Q + R + ΔS w [1] Where P is precipitation and is the largest term in the water balance equation, varying both temporally and spatially. It is partitioned into evapotranspiration (E), overland flow (Q), recharge to the ground water (R) and the change in soil water storage (ΔS w ). Evapotranspiration is generally the second largest term in the water balance equation and is closely linked to vegetation function. In arid regions, E can be almost equal to P, but in humid tropical regions E tends to be much less than P. The water balance of a site depends critically on a number of site specific parameters that concern the physical properties of the soil and vegetation and the meteorological conditions. Although these tend to be less important at very large catchment scales, at medium and smaller site scales, the role of vegetation dynamics plays a greater part in determining the water balance. Evaporation is directly influenced by canopy conductance (a measure of how easily water can move out of the canopy), net radiation (the energy source that drives evaporation), vapour pressure deficit (the evaporative demand of the air) and plant available water (Jarvis and McNaughton, 1986, Wullschleger and Hanson, 2006, Zeppel et al., 2008a, Zeppel and Eamus, 2008). Under different conditions of meteorological forcing, some drivers become more apparent than others. For arid ecosystems (water limited systems), canopy conductance and plant available water are the more dominant determinants of vegetation water use, as trees will close their stomata in order to conserve water. In 3

4 sub tropical wet regions, net radiation, leaf area and wind speed become more dominant, as there is insufficient available energy to evaporate all the water (Budyko, 1974, Zhang et al., 1998). Meteorological drivers of evapotranspiration The primary pathway by which water moves through vegetation is referred to as the soil-plant-atmosphere continuum (SPAC). Transpiration (being part of this pathway) is the major component by which water (and sometimes energy) leave the forest ecosystem. An awareness of this at a spatial and temporal scale is important in determining the water budget of woody landscapes (Eamus et al., 2006). When forest canopy water fluxes are known, along with the drivers of transpiration, it is possible to calculate canopy conductance, which represents an important parameter in many water and carbon exchange models. These models are linked due to the common passage of water vapour and CO 2 through through the leaf s stomata. A tree s water flux through the SPAC can be described as principally driven by three environmental variables, namely: net radiation of the site the vapour pressure difference (D) between the leaf and the air, and the water content of the soil (Jarvis, 1976, Stewart, 1988, Wright et al., 1995). The figure shows the relationships between transpiration and its three major driving variables. Seasonal variations cover canopy transpiration and canopy conductance (Harris et al., 2004, Komatsu et al., 2006). Measuring seasonal variations of these abiotic (physical, that is, not biological) variables and parameterising their impact on transpiration, is important for quantifying intra-annual variation in forest water use. The figure at left shows the asymptotic relationship between transpiration and solar radiation. As solar radiation increases, light begins to saturate the canopy and the supply of energy for the evaporation of water through the leaf stomata becomes non-limiting. Thus transpiration increases steeply at low levels of light but the slope declines as the availability of energy increases. At some point any further supply of radiation will only give a small rise in transpiration, as the tree is physically limited by its own hydraulic architecture (namely the ability of the xylem to conduct water to the canopy). The middle graph below shows the relationship between transpiration and D. This response is observed because of the three-phase behaviour of stomata in response to increasing D (Monteith 1995; Thomas and Eamus 1999; Eamus and Shanahan 2002, Pataki et al., 2000; Komatsu et al., 2006b). It is the result of a feedback between increasing cuticular water loss (water lost through the waxy coating on the outer surface of leaves) as D increases and a declining supply of water to guard cells (Eamus et al., 2008). Starting at low levels of D, as D increases, transpiration increases because the evaporative demand for water can be supported by the ability of the roots and stem to supply water to Emax Transpiration (a) (b) (c) Solar Radiation Vapour Pressure Deficit Soil Water Content The three relationships between transpiration, solar radiation, vapour pressure deficit and soil water content. The blue dotted line represents the maximum value of transpiration.. 4

5 the canopy. At moderate values of D, the supply of water to the canopy equals the demand for water but the supply has reached a maximum rate. As D increases beyond this point the canopy begins to close it s stomata to prevent the canopy becoming water stressed (the supply of water to the canopy is less than the rate of loss). The righthand graph shows a piece-wise or broken stick relationship between transpiration and soil water content (SWC). In many sites in Australia this can be a critical parameter in many water balance models, although significant exceptions occur whereby canopy water use appears to be relatively insensitive to changes in soil moisture content in the upper profile (up to 1 m depth) of soil. This relationship is site dependent and shows large variation across different soil types, which makes establishing a broad relationship between transpiration and SWC across sites and ecosystems difficult. Methods of estimating stand-scale water use at daily, monthly and annual time-frames The Penman-Monteith model Over the past 50 years, the physics of evapotranspiration has become well understood. One of the most commonly used equations for estimating evapotranspiration is the Penman- Monteith equation (abbreviated as PM), which represents the evaporating surface as a single big leaf and is based on a combination of energy balance and mass transfer formulae (Eagleson, 2002). Two key parameters incorporate the role of vegetation in determining evapotranspiration, namely: the aerodynamic conductance, which is a measure of the resistance to diffusion of water through the boundary layer around leaves and which is influenced by wind speed and canopy architecture (especially the degree of openness of the canopy), and the surface conductance, which is to a large extent determined by the degree of stomatal opening exhibited by the leaves, which in turn depends on soil moisture content and the meteorological conditions (especially solar radiation and D) (Monteith, 1965). Thus, the PM equation is a relatively simple representation of the physical and physiological factors governing the evapotranspiration process, and has been widely applied to many different vegetation types, such as crops and grasslands (Yunusa et al., 2000, Lu et al., 2003) and forests (Gash et al., 1989, Kosugi et al., 2007, Zeppel et al., 2008a). The PM equation is given as: where R n is the net radiation (closely correlated with solar radiation), G is the soil heat flux, D is the vapour pressure deficit of the air, r is the mean air density at constant pressure, c p is the specific heat of the air, Δ represents the slope of the saturation vapour pressure temperature relationship, is the psychometric constant. Aerodynamic conductance (g a ) is defined as the transfer of heat and water vapour from the evaporating surface into the air above the canopy and is formulated as: E is canopy latent heat flux, which is the transpiration rate multiplied by the latent heat of vapourisation where k is the von Karmen s constant (0.4), U is the wind speed (m s -1 ), z m is the height of wind measurement (m), z om is the roughness length governing momentum transfer, z h is the height of humidity measurement (m), z oh is the roughness length governing the transfer of heat and vapour (m), and d is the zero plane displacement height (m). The bulk surface conductance (g s ) describes the vapour flow through stomatal openings, total leaf area and soil surface. * There are many models available to estimate stomatal conductance. Some have been developed that estimate a maximum stomatal conductance value (Kelliher et al., 1993, Schulze et al., 1994, Kelliher et al., 1995). However these do not incorporate effects of limited soil water availability or stomatal physiology. Including such characteristics requires a more coupled biophysical model such as Tuzet et al., (2003) or an empirical model such as that of Jarvis, (1976) and Stewart, (1988), both of which must be calibrated. The Jarvis-Stewart model (abbreviated as JS), is a purely empirical model of bulk stomatal conductance ( ĝ s ), whereby a bulk maximum stomatal conductance parameter ( ĝ s max ) is [2] [3] * Both g s and g a are the inverse of surface (r s ) and aerodynamic resistance (r a ), and operate in series with one another. 5

6 proportionally modified by a set of scaling functions, defined as: where the functions (f 1, f 2, f 3 ) represent a set of non-limiting relationships between stomatal conductance, solar radiation (R s ), vapour pressure deficit (D) and soil moisture content ( ). LAI represents the leaf area index and its incorporation is to scale the maximum stomatal conductance to a maximum surface (canopy) conductance. The functions themselves contain a set of free parameters which are calibrated to fit the functions to the data in question. JS models have been used extensively because of their simplicity and they allow calculation of g s as a function of readily available meteorological and soil moisture data (Jarvis, 1976; Wright et al., 1995; Whitehead, 1998; Harris et al., 2004; Komatsu et al., 2006a, b; Ewers et al., 2007). However, at larger spatial (regional) and temporal (monthly, yearly) scales these models are not practical. The PM equation may be simplified further, through the sensitivity of E to changes in g a and g s. If g s g a, then E is limited by the surface conductance, and so Equation 2 becomes: [4] [5] For wet surfaces, such that g s g a, Equation 2 reduces to the equilibrium evaporation rate: where the only limitation to E is the available energy (R n +G). The sensitivity of E to (R n +G) increases with increasing g a, hence the PM equation is only sensitive to wind speed (through g a ) when surface conductance is large. The full PM equation provides the most robust approach to estimating evapotranspiration, as it combines the main drivers of E in a theoretically sound way, is not overly sensitive to the driving variables, and has been successfully and widely applied so much so that it is the United Nations Food & Agriculture Organisation s (FAO) standard for modelling evapotranspiration. There is evidence, however, that it tends to overestimate evapotranspiration in water limited environments. [6] Remote-sensing and the Penman-Monteith model The PM equation has been applied successfully to many ecosystems. However, scaling the PM model to larger spatial and temporal scales has not been widely investigated. The problem lies with defining g s at large scales, without the need for complex parameterisations. The idea behind a remote-sensing Penman-Monteith (denoted as RS-PM) model is the ability to estimate latent energy fluxes (latent energy fluxes are the fluxes of energy arising from the evaporation of water from a liquid phase to a vapour phase) using readily available data from satellite sources. The following are two methods that have been proposed. The Cleugh method Cleugh et al., (2007) propose a method of applying the PM equation to 1 km and continental spatial scales using surface meteorology measurements and remote sensing data. They also suggest a simple model for calculating g s at these larger scales using remote sensing data. The PM equation is applied in its full form, thereby retaining the energy balance restraints that make it a robust model, the difference is in how the surface conductance is calculated for weekly and monthly time-steps. Because most g s models, such as those developed by Jarvis, (1976) and Kelliher et al., (1995), require re-parameterisation over different sites, their applicability is lacking. However, Cleugh et al., (2007) suggest that LAI, normalised difference vegetation index (NDVI), and the fractional vegetation cover (F C ) are adequate surrogates for g s. These a priori assumptions are based upon the following relationships: the development of a vegetated land surface requires soil moisture to be available, long-term (years) differences in soil moisture between sites will be reflected by long-term differences in LAI, NDVI and F C, and at the time-scale of several weeks or longer, fluctuations in soil moisture will be reflected in changes in NDVI. Hence, low values of g s are expected at low values of LAI and low soil moisture, while the inverse is true as well; high values of g s, expected at high values of LAI and soil moisture. Following this line of reasoning, Cleugh et al., (2007) have suggested the following model for g s based on the assumption that soil evaporation is negligible 6

7 compared to plant transpiration such that g s g c (g c being canopy conductance). Hence, the model is defined as: [7] where c L is the mean surface conductance per unit leaf area index, g s min is the surface conductance controlling soil evaporation and conductance through the leaf cuticle (generally g s min = 0), and F C is the fractional vegetation cover and is defined as: [8] Cleugh et al., (2007) found that the parameter c L was remarkably similar for their two sites of study despite their different vegetation types and climate; c L = for the tropical wet savannah and c L = for the cool temperate forest; both explaining 74% of the variance in the measurements of the two sites. Further investigation revealed that an average c L value still explained 74% of the variance, suggesting that Equation 7 may have broad applicability. Cleugh et al., (2007) showed that for both sites at local spatial scales there was a good agreement between estimates from the RS-PM model and measured data using their linear surface conductance model. This model was subsequently applied to data from non-local sources, such as those from the Australian Bureau of Meteorology, and compared against outputs from the RS-PM model using local measurements. The RS-PM was shown to hold up sufficiently well with only a slight decrease in performance, with the explained variance dropping form 74% to 73%. Finally the RS-PM approach was applied to a continental scale, with estimates of E comparing well with the climatological averages of evapotranspiration provided by the Australian Bureau of Meteorology s Morton model. The Mu method Following the methodology of Cleugh et al., (2007), Mu et al. (2007) formulated an improvement to the RS-PM model. Two concerns are raised concerning the RS-PM s linear surface conductance model of Cleugh et al. (2007). These are: Two assumptions are required first: that that g s =g c ; and second, soil evaporation can be neglected; Only when both assumption are valid can LAI and NDVI be used to calculate g s. There are no constraints concerning plant water stress or temperature on canopy conductance. The first concern is especially valid when LAI is low and there is a high ratio of soil evaporation to evapotranspiration. However, this is only a problem when the soil surface is wet as soil evaporation rapidly declines to zero within a day or two after rain. Ecosystems that have a consistently low LAI are arid and therefore the number of rain days per year is small and therefore the contribution of soil evaporation to total evapotranspiration is likely to be small. Their second argument is more problematic because the absence of a soil moisture response function to canopy conductance will lead to an overestimation of transpiration during dry periods (Mu et al., 2007). In order to overcome these two issues, Mu et al., (2007) partitioned the calculation of evapotranspiration into separate components of canopy transpiration and soil evaporation. This has resulted in a re-formulation of the linear surface conductance model presented in Equation 7 and the replacement of NDVI with enhanced vegetation index (ENI). We will denote the combination of both canopy and soil estimates as the Revised RS-PM model. They proposed that as many plant species experience a decrease in canopy conductance as D increases, and is further limited by both low and high temperatures, g c may be expressed as, [9] where c CL is the mean canopy conductance per unit leaf area, m(t min ) and m(d) are multipliers that limit potential surface conductance by minimum temperature and vapour pressure deficit respectively. m(t min ), given as: [10] where T open is the temperature at which transpiration is not inhibited, and T close is the temperature at which it is. m(d) is a multiplier used to reduce surface conductance when D is too high for stomatal opening and given as: 7

8 [11] where D open is the D at which transpiration is not inhibited, and D close is the opposite (the D at which transpiration is limited). Fractional vegetation cover is redefined to be a function of EVI, for reasons that are too lengthy to state here (see Mu et al., 2007), and so EVI replaces NDVI in Equation 8. F C is then used to partition net radiation into both canopy and soil components, in order to calculate the evaporation components of canopy and soil separately. Mu et al., 2007 have shown that the Revised RS-PM model performs better than the RS-PM model, substantially reducing the root mean square error (RMSE) by almost 60%. The revised RS-PM model has also shown a slight decrease in performance when replacing local flux data with non-localised measurements, with explained variance dropping from 76% to 70%. Finally the Revised RS-PM was applied at a global scale, and was found to agree well with MODIS observations. The Leuning method Leuning et al. (in press), have developed a more refined method for applying the PM equation to large-scale analysis that overcomes some of the short-falls of both the methods of calculating surface conductance, developed by Cleugh et al., (2007) and Mu et al., (2007). Leuning s method introduces a new model for surface conductance that is based on the surface conductance model proposed by Kelliher et al., (1995) which replaces the g s model used in the Cleugh and Mu methods (Eq. 7 & 9). Additionally a much simpler soil evaporation model than that used by Mu et al., (2007) is incorporated in Leuning et al. Evapotranspiration is the sum of transpiration from the canopy (E c ) and evaporation from the soil (E s ), such that E = E c + E s. Leuning et al. have expanded Equation 2 to include a soil evaporation component, e /e +1, which assumes that evaporation from the soil, occurs at some fraction (ƒ) of the equilibrium rate at the soil surface. Evapotranspiration can therefore be expressed as: [12] where e = Δ /g, represents the partitioning of the available energy ( A=Rn-G) into canopy (A c /A= -1) and soil components ( A s /A= ) respectively and is formulated as, =exp(-k A LAI ), where k A is an extinction coefficient for available energy and LAI is leaf area index. The parameter g i is the climatological conductance as defined by Monteith (1965) and is expressed as, g i =A/( c p / )D. From here Leuning et al. re express Equation 12 in terms g s, such that: [13] Although this expression of g s looks rather horrendous it can be reduced to much simpler forms by describing several useful limits of 0 < < 1 and 0 < ƒ < 1, which pertain to various land surface types, i.e. ƒ=0 would describe a surface that is completely dry and =1 when there is full canopy cover and the model reflects grass or crops (Leuning et al. in press). The formulation of the canopy conductance model is a modification of that developed by Kelliher et al., (1995), introducing a component that expresses the influence of D on g s. The canopy conductance is expressed as: [14] where, Q h is the visible radiation at the top of the canopy (50% of solar radiation), D is the vapour pressure deficit, LAI is the leaf area index, g sx is the maximum stomatal conductance of leaves at the top of the canopy, k Q is the extinction coefficient for short-wave radiation and Q 50 and D 50 are the visible radiation flux and D at half of the maximum stomatal conductance respectively. We therefore end up with 6 free parameters g sx, k A, k Q, Q 50, D 50 and ƒ, which when substituted with Equations 13 and 14 into the PM equation, are optimised for the study period or site. Leuning et al. (in press) applied their model to 15 flux station sites from around the world. These sites covered a wide range of climate and vegetation ecosystems such as deciduous and evergreen forests, corn crops, wetlands, grasslands and woody savannas. For each flux site, the six free parameters of the model were optimised over two to three years of data. 8

9 Subsequently, average values for k A, k Q, Q 50 and D 50 were then used and held constant, and only g sx and ƒ were optimised, to simplify the model, which resulted in no significant reduction in performance. Regressions between modelled and measured data showed a range of explained variance between 83 96% and root mean square error range of mm d -1. The results from this study further confirm that the PM equation is a reliable model in estimating evaporation rates from land surfaces over large spatial and temporal scales. A modified Jarvis-Stewart model Whitley et al. (2008) have formulated a simplification of the PM equation in order to estimate evapotranspiration without the need of surface conductance, and uses only three readily available environmental variables, namely solar radiation, D and soil moisture content. The logic is as follows: for a well-coupled forest, E can be calculated from g s and D (Equation 5). Since g s =ĝ s LAI, where LAI is leaf area index and ĝ s being stomatal conductance, and if we allow for a negligible effect of aerodynamic conductance on transpiration (that is, g a g s ), then we can reexpress the PM equation for surface conductance as a function of its driving environmental variables (Jarvis, 1976; Whitehead, 1998), thus: [15] which is equivalent to Equation 5. Following the formulation given above, two modifications are made to Equation 12 to directly estimate E and remove the need to know g s. In keeping with the approach of empirically defining the stomatal conductance as formulated by Jarvis, (1976) and Stewart, (1988), we express E in the same way. This modified version of the JS model (which we denote as M-JS) is defined as: [16] E is proportionally modified by a set of discount functions, assuming values between 0 and 1. The functions themselves are described as the relationships between (i) evapotranspiration and solar radiation (Figure 1a): [17] where R s is the solar radiation, 1000 is the plateau of the asymptotic saturating function which was derived by Jarvis, (1976) and has been subsequently used since, and k 1 is a site specific free parameter; and (ii) evapotranspiration and D: [18] where D is vapour pressure deficit, and the free parameters k 2 and k 3 roughly denote the point of regime A described by Monteith, (1995) and subsequently by Thomas and Eamus, (1999), Eamus and Shanahan, (2002) and Eamus et al., (2008); and (iii) evapotranspiration and soil moisture content: [19] where θ is the soil moisture content, and θ w and θ c are free parameters and denote the wilting point and critical points respectively. Equation 12 is a broken stick function commonly used to describe a site that experiences water stress. Equations 14, 15 and 16 act as scaling terms, that reduce a bulk maximum evapotranspiration term for a site (denoted E max ), down to an actualised value. The model is parameterised by optimising the free parameters E max, k 1, k 2, k 3, θ w and θ c using a non-linear least squares method. Whitley et al., (2008) have shown a good agreement between model and measured data, with the model explaining 90% of the variance. Furthermore, the model was parameterised over a short-term period, and shows promise in determining long-term predictions of tree water use. The M-JS model is functionally equivalent to the PM equation, yet is much simpler to fit, requires fewer measurements and specifically avoids the need to estimate stomatal conductance, as has been applied in the past (Ewers and Oren 2000; Lu et al., 2003; Pataki and Oren 2003). The Budyko curve The Budyko curve (Budyko, 1974) describes the relationship between a mass balance and energy balance at catchment scale. Conceptually, the Budyko curve considers a catchment as a lumped bucket; water goes into the bucket as rainfall (P), water is stored in the bucket (S w ), and water leaves the bucket through evapotranspiration (E) and runoff (Q). We can also consider this bucket model in terms of energy as well; energy goes in the bucket as net radiation (R n ), energy is stored 9

10 in the bucket (S e ), and energy leaves the bucket as latent ( E) and sensible heat (H). becomes energy limiting as there is not enough available energy to evaporate water at the rate of rainfall. Budyko, (1974) developed a model to estimate evapotranspiration based on the relationship of available water and energy, and constrained by the limits of these two variables. Thus: Conceptualisations of the bucket model in terms of (a) water balance and (b) energy balance. We formulate two balance equations in terms of the water balance of the catchment and the energy balance of the catchment. For the water balance and storage, the catchment receives rainfall at a rate P(t), loses water through evapotranspiration at a rate E(t), and through fluxes of surface runoff at a rate Q(t), We define the water balance as: [20] In terms of energy balance and storage, the catchment receives energy in the form of net radiation at a rate R n (t), and loses energy through latent and sensible heat at rates E(t) and H(t) respectively. We define the energy balance as: [21] where is the latent heat of vaporisation. We consider an annual water balance, where there is negligible change in soil water storage, i.e. ds w,e / dt = 0, such that P = E + Q. For the energy balance we also assume no storage of heat over an annual time frame and R n = E+H. As the energy supplied (R n / ) to the catchment increases, evapotranspiration begins to increase and will eventually be greater than (if groundwater or lateral run-on of water is available) or equal to the amount of rainfall entering the system. At this point the system becomes water-limiting; all water falling into the catchment is evaporated back out and none is stored. Conversely, as less energy becomes available to the system to evaporate incoming rainfall, more water is stored and will eventually overflow to give runoff. Hence the system Evaporative Index (ε) [22] The following figure shows the form of the Budyko curve and how evapotranspiration reaches one of these two limits, with the dashed line AB defining the water limit to evapotranspiration, and the dashed line CD defining the energy limit to evapotranspiration. The degree of limitation is described by a radiative index of dryness ( ) which is a ratio of R n / to P, where >1 represents water limited environments, <1 represents energy limited environments and 1 represents intermediate environments (Budyko, 1974). An evaporative index (ε = E / P ) parameter is used to describe the partitioning of P (precipitation) into E (evapotranspiration) and Q (runoff). Both Q and H are proportional to the vertical distance from the curve to the energy and water limits respectively A C Budyko Curve Dry Index (φ) A representation of the Budyko curve. D The performance of the Budyko curve has been reviewed on many performance affecting factors such as scale, the role of vegetation and deviations from the curve itself (Choudhury, 1999). Budyko, (1974) found that for large catchment areas (A c > 1000 km 2 ), the macroclimate was the principal factor in determining evapotranspiration. However, as the catchment scale becomes much smaller, and hence our resolution becomes larger, local We divide R n by the latent heat of vaporisation (2.49x10 9 J m -3 ), in order to convert the available energy for evaporation into depth of water evaporated. B 10

11 conditions such as vegetation and topography give larger variation in evapotranspiration due to the sensitivity of R n at this scale (Donohue et al., 2007). A relationship between the water and energy balance of a catchment in terms of its size and depth of storage can be drawn by integrating equations 17 and 18 over a finite time space ( ) that keeps with steady-state conditions (Donohue et al., 2007). Again, we go back to our simple bucket model and by considering the volume of the bucket, we introduce a depth term (z) and catchment surface area (A c ) to the equation, and so the mass balance (Equation 17) can be reformulated as [23] and the energy balance (Equation 18) becomes: [24] The parameters A c and respectively determine the spatial and temporal scales of the analysis, z r determines the total possible soil water storage or rooting depth and z e determines the depth of energy storage. The reasoning behind formulating the energy and mass balances equations in this way is to draw links between vegetation characteristics of the catchment and the spatial scale of the analysis and create a link between the flux and steady-state components of the relationships (Donohue et al., 2007). From these relationships Choudhury, (1999) and Zhang et al., (2001) have reformulated Budyko s curve to deal with scale and vegetation more explicitly and will be discussed in the next two sections. The Choudhury method Although not directly concerned with vegetation dynamics at smaller catchment scales, Choudhury, (1999) explored the effects of the spatial scales (A c ) on predictions of evapotranspiration. [25] Choudhury s, (1999) curve is based on the equation developed by Pike, (1964) with the difference of an adjustable parameter. The parameter allows for the equation to change at different spatial scales, because of the spatial variation of R n and P at different scales. Equation 22 also acknowledges that evaporation may occur from different types of vegetation at a site. Choudhury, (1999) found that the dependence of E on P and R n changed with A c, with being large at site based scales ( =2.6) and decreasing to lower values at basin level scales ( =1.8); the large the basin, the lower the, and therefore less evapotranspiration for a given dryness index, F = R n / P (Choudhury, 1999; Donohue et al., 2007). The Zhang method Zhang, (1998) and Zhang et. al. (2001) took a more focused approach on the role of vegetation in the Budyko curve and evapotranspiration. Key vegetation characteristics affect rates of evapotranspiration, and so the Budyko framework was modified to quantify the long-term effects of changing vegetation on evapotranspiration. He formulated the following equation: [26] Equation 26 is a modification on Budyko, (1974) and Choudhury s, (1999) work. It introduces an adjustable term,, denoted as the plantavailable water coefficient. The plant-available water coefficient symbolises the total water available to the plant within the root zone for transpiration (Zhang, 1998). Hence, reflects the integrated role of multiple catchment processes on evapotranspiration; with notable reference to the depth of water storage (z r ) on E (Equation 20). Zhang, (1998) notes, that for forests =2.0, for crops and grasses =0.5, and for bare soils =0.1; as increases, the larger the role of vegetation in evapotranspiration. At the limiting ends of the Budyko framework of water ( ) and energy stress ( 0), Zhang (1998) noted the minimal effect of on evapotranspiration, and that is very sensitive to intermediate values of dry index,»1 (Zhang et al. 2001; Donohue et al., 2007). On a final note, Donohue et al., (2007) suggest that care must be taken when applying the Budyko curve to smaller temporal scales ( <1 yr), as the vegetation is likely to experience greater variation (i.e. drought, bush fires, harvesting, deforestation) and therefore show greater variation in S w. Vegetation dynamics can therefore 11

12 present non-steady-state conditions, and if it is necessary to increase the time scale ( >1 yr), then the application of these models becomes less and less appropriate to areas of catchment and land management. The Soil-Plant-Atmosphere model The soil-plant-atmosphere continuum (SPAC) is a complex process of interactions between hydrology, vegetation processes and micrometeorology. There are many SPAC models. The SPA model of Williams et al., (1996) is a process-based model that simulates ecosystem photosynthesis and water balance at fine temporal and spatial scales. It has been applied to model eddy-flux data and as a tool for scaling up processes at the leaflevel to canopy and landscape levels. The SPA model focuses on canopy processes, and explores links between leaf-level water loss, leaf and soil water status, and water fluxes from the soil through the plant. Additionally, it simulates soil surface energy balance, soil heat and water transport, root distribution and water uptake, and the interception and evaporation of water on canopy surfaces (Williams et al., 2001a). SPA has been successfully tested and validated across a range of diverse ecosystems, including Brazilian tropical rainforests (Williams et al., 1996, Williams et al., 1998), Arctic tundra (Williams et al., 2000), temperate Ponderosa pine forests (Williams et al., 2001b) and native Australian woodland (Zeppel et al., 2008b). The model works, by partitioning the forest canopy into 10 layers, and has a time-step of 30 mins. These 10 layers describe the vertical variations in the canopy for light-absorbing leaf area, rate of photosynthesis and hydraulic properties. SPA incorporates a comprehensive radiative transfer scheme, whereby the canopy is divided into sunlit and shaded foliage (Williams et al., 1998). The leaf level processes are determined by an optimised stomatal conductance algorithm, and the soil energy and water balances are determined from the soil profile partitioned into numerous layers. Because SPA has too many routines to be discussed here, we shall look at one feature of SPA, its stomatal conductance algorithm (for further information see Williams et al., 1996, Williams et al and Williams et al. 2001a) The algorithm works by adjusting the stomatal conductance to balance the rate of water uptake from the soil with the atmospheric demand and to maximise photosynthesis. Water-loss is calculated using the PM equation, and is linked with changes in the leaf water potential, such that: [27] where E t is transpiration (water-loss), s and l are the soil and leaf water potentials respectively, and R is the total hydraulic resistance. In order to prevent cavitation of the hydraulic system, transpiration is maintained at a rate that remains above a (user defined) critical threshold value of leaf water potential ( l min) (Williams et al., 1996). When = lmin, then E t is set so that d l /d t = 0, and is given as: [28] Where, w is the density of water, g is the gravitational constant, h is the height above the reference plane and C is the hydraulic capacitance. A problem with SPA is that it is very parameter heavy; requiring an extensive knowledge of vegetation dynamics and parameters of the study site in question. This necessitates detailed field studies in order to calibrate the model s parameters. There is also an issue with the assimilation routine, which only assumes C 3 vascular processes. This is not a problem for most northern-hemisphere forests; however much of the Australian continent contains a significant biomass of C 4 grasses. It is unclear whether this has an effect on the water balance routines of the model. Methods for measuring water fluxes through the soil-plant-atmosphere continuum The principal pathway for the release of soil water to the atmosphere is through vegetation. To determine the water budget of catchments and woody landscapes, tree canopy water fluxes must be known, either through direct measurement or through modelling (Komatsu et al., 2006a; Wullschleger et al., 2006). As has been described, tree water fluxes are driven by many variables such as canopy conductance, solar radiation, 12

13 vapour pressure deficit and soil water availability (Jarvis and McNaughton, 1986; Wullschleger and Hanson, 2006; Zeppel et al., 2008a). Hence, seasonal variations in these variables cause seasonal variation of canopy transpiration (E c ) (Komatsu et al., 2006b). It is therefore important to measure the seasonal variations of these driving variables and parameterise their impact on E c, in order to quantify the intra-annual variation in E c. Below we give a brief description of the three major ways of measuring canopy water fluxes. Sapflow techniques Sapflow is the movement of water through a plant s xylem, and the rate of water moving through the soil-plant-atmosphere pathway equals the amount of water vapour leaving the canopy. There are three primary methods of measuring the volume of water moving up the stem, i) heat pulse, ii) thermal dissipation, and iii) stem heat balance. These are now discussed. Heat pulse The heat pulse method measures the instantaneous sapflow velocity moving through a point within the xylem of the stem. To estimate whole-tree water use, this sap velocity is converted to a volume of water by using sapwood area and volumetric sapwood water and wood content. Transpiration of an entire stand can be estimated by scaling the direct measurements of water-use of individual trees using sapwood area or leaf area. The technique involves inserting three sensors into the tree s stem. The middle sensor contains a heater and the upper and lower sensors contain thermocouples which measure the temperature of the xylem above and below the heater. The central probe releases a pulse of heat every 15 minutes, and the time taken for the pulse to travel the distance to both sensors is recorded. From this measurement of the velocity of the heat pulse, plus measurements of the sapwood cross sectional area and volumetric water and wood content, the rate of flow of water up the stem can be calculated. Three probes inserted into the xylem of a tree are used in a heat-pulse system. Thermal dissipation Dissipation is the second major method used to measure sapflow and was developed by Granier, (1985). Principally Granier s method works in a similar way to the heat pulse method, except that instead of short pulses of heat used on the xylem sap, the xylem sap is continuously heated. The temperature difference between the heating probe and temperature probes is a function of sapflow density passing the heat source. Granier, (1985) gave the function to be, [29] where v S is sapflow, A S is the sapwood area, T m is the maximum temperature difference when sapflow is zero (must be obtained at night), and T d is the actual temperature difference at sampling time. Stem heat balance The last of the three methods uses an external heat source. This technique is non-destructive as no drilling into the xylem is required. Heat is continuously supplied to the stem, and the temperature of the stem above and below the heat section is measured. Using a heat balance equation the sapflow of the stem is determined as, [30] where Q h is the heat input to the stem, Q r is the heat lost radially, Q v is the heat lost vertically, Q s is the heat stored in the stem, c s is the heat capacity of the sap, and T is the temperature 13

14 difference between top and bottom of the heated stem section. Excessive continuous heating of the stem must be avoided as it may kill the plant and good thermal contact must be made between heater and stem (Eamus et al., 2006). The volume of water moving up through the xylem is calculated by multiplying the velocity of sapflow (v S ) by the sapwood area (A S ) and V Sw. The tree water flux (E t ) can then be expressed as, [31] The use of sapflow sensors has had an important impact on the study of tree wateruse, water balance and ecohydrology over the past 20 years (Eamus et al., 2006). The use of sapflow sensors has allowed for the study of many tree water-use issues, such as the daily and seasonal patterns of transpiration, the variation of transpiration with changes in meteorological forces and soil water availability, relationships between transpiration, hydraulic architecture and climate, and finally, estimating catchment scale water-use from scaling up estimates of tree scale water-use (Eamus et al., 2006). Eddy covariance Eddy covariance (EC) is a micro-meteorological approach of estimating evapotranspiration and CO 2 uptake from large areas of vegetation (1-2 km 2 ). The area of land being measured by EC is commonly referred to as a footprint (we will now refer to the ground area below as a footprint). Data are collected frequently (every 30 minutes) and the approach can be applied to short and tall canopies. Measurements of fluxes over the footprint are averages, and hence only total evapotranspiration is collected, as the measurements cannot distinguish individual components such as soil evaporation and transpiration. EC relies on the turbulent flow of air above and through the forest canopy, and the wind at any single point above the canopy considered to move stochastically, due to the large number of eddies comprising the flow of wind. The EC system consists of three major components which act together to take separate measurements of the same eddy of air ; i) the open-path infra-red gas analyser (OPIRGA), which measures the Although it is not possible to record measurements from the exact same eddy of air, we theoretically assume them to be the same. flux concentration of water vapour and CO 2 at a single point, ii) the 3-dimensional (3D) sonic anemometer, which measures the velocity of air by sending out an ultrasound pulse in all Cartesian coordinate directions to detectors placed close to the OPIRGA, iii) a temperature sensor, which measures the temperature of the air being sampled. Additionally a net radiometer is placed above the canopy which measures net radiation, and soil heat flux plates are installed below ground to measure the heat fluxes at the soil surface. Large amounts of data are collected for windspeed, CO 2 concentration, temperature and water vapour concentrations at a frequency of 10 Hz. The 3D sonic anemometer integrates all these measures into upward and downward components of air movement. Thus, equivalent concentrations of CO 2 flux and water vapour are recorded. The measurements are an average or bulk estimate of the footprint; there is no independent measure of vegetation and soil evaporation rates. The EC system must be placed a significant distance downwind of a relatively homogenous canopy structure on a flat terrain. Depending on the height of the canopy in question, the distance will vary (1-2 km for woodlands and 500 m for grasslands). This distance is necessary so the wind travelling over the footprint has had time to equilibrate with the canopy (Eamus et al., 2006). Several sources of error are prevalent in EC measurements, and may be referred to further in Hutley et al., (2001) and Medlyn et al. (2007). The EC system of measurement has been applied successfully to large number of sites around the world, including boreal (Baldocchi, 2003, Granier et al., 2000, Wood et al., 2008), temperate (Sacks et al., 2006), tropical rainforest (Williams et al., 1998) and savannah ecosystems (Hutley et al., 2000). Scintillometery A major concern with EC measurements is the lack of energy balance closure that may be observed above tall vegetation. Both gas and heat fluxes measured by EC can be prone to underestimation errors, with possible causes of the problem being the shortage of fetch, a mismatch of net radiometer and eddy covariance footprints and a difference of instrument error or response characteristics (Nakaya et al., 2007). However, none of these reasons are sufficient enough to explain the observed lack of energy 14

15 balance closure. New optical methods of measuring turbulence, such as scintillometery, are therefore generating significant attention in measuring land surface water fluxes. A scintillometer consists of a transmitter emitting electromagnetic radiation towards a receiver within a range of 50 m to 50 km of separation. The scintillometer is installed above the vegetation surface and sensible heat flux is derived by measuring the scattering of the electromagnetic radiation caused by the turbulence of the air. This turbulence is due to small fluctuations of the refractive index of air caused by caused by variations in temperature, humidity, and pressure. The sensible heat flux is used to calculate evaporative water fluxes using measurements of available energy provided by a complimentary Bowen ratio system. From this system, evapotranspiration can be determined from the energy balance equation defined as, [32] where E is evapotranspiration, R n is net radiation, G is the soil heat flux (in most cases close to zero), H is the sensible heat flux, and the latent heat of vaporisation. Scintillometery has been applied across a number of different environments such as African savannas (Marx et al., 2008) and deciduous forests (Nakaya et al. 2006). Conclusions Understanding the water budget of landscapes is a prerequisite for successful sustainable management of water, vegetation and land resources. Transpiration of vegetation is the single largest pathway for the discharge of water from Australian landscapes and the rate of transpiration is determined by solar radiation, leaf area index, vapour pressure deficit and soil moisture content. A number of contrasting methods of modelling rates of transpiration are available to managers and researchers, including the Penman-Monteith equation and the Jarvis-Stewart approach. The conceptual frameworks and application of the Budyko, Choudhury and Zhang methods and application of remotely sensed methods are also widely applicable, although the latter is not yet widely used except as a research tool. This will change in the near future. Several field-based methods of measuring tree and landscape water use, including sapflow techniques, eddy covariance and scintillometery are widely used, although scintillometery is still only a research tool in Australia. However, it is possibly the simplest of all techniques to install in the field. The laser source for a scintillometer. 15