## Q

canopy resistance, rc

Figure 2: Modelled values of the omega factor (Q) as a function of canopy resistance, for different values of aerodynamic resistance.

canopy resistance, rc

Figure 2: Modelled values of the omega factor (Q) as a function of canopy resistance, for different values of aerodynamic resistance.

### 2.2 Methods to Measure ET in Stands of Woody Plants

The methods for ET measurement that have been currently used, in field conditions, can be classified in two main categories: hydrological and micrometeorological methods.

Hydrological methods are based on the application of the water balance equation, where all the variables are measured or estimated and ET is calculated. It can be applied at different spatial scales from the small lysimeter to the watershed. The temporal scale is dependent upon the spatial scale used. The use of lysimeters with woody crops is limited by the large dimensions required and by the inherent high cost, since heterogeneity between plants is often important. One single plant or a few plants usually cannot be considered representative of a stand, as indicated by experimental evidence when analysing individual tree behaviour using sap flow methods (Granier, 1987; David et al., 1996, among others). The use of the water balance equation at the canopy level is limited in trees by lack of accessibility to the deep root zone and the spatial heterogeneity of roots distribution. Furthermore, due to the poor measurement precision, it is not possible to follow ET on an hourly or even daily time scale which is needed for detailed analysis of plant behavior (Rose and Sharma, 1984; Rosenberg et al., 1983). Most applications of the water balance equation at the watershed scale require even larger time scales (Villagra et al., 1995).

For a temporal detailed analysis, micrometeorological methods are usually preferred. ET is measured from meteorological variables, observed with appropriate time interval (< 0,1 s to > 2 min) at one level (eddy covariance, EC) or two levels (based on flux-gradient relationships: Bowen ratio, aerodynamic or combinations) above the surface, using equations that describe the fluxes of water vapor in the atmosphere. Continuous data recording is necessary. These methods are applicable over large and homogeneous surfaces, in order to meet assumptions in the theory and avoid advection effects. The minimum required distance from the measurement point to the edge of the plot being measured depends upon the measurement height; it is common to consider roughly the value of 100:1 horizontal to vertical measurement height (Brutsaert, 1982), but foot-print analysis (Schuepp et al., 1990) provides more realistic fetch requirements. The measurement level depends on the plant height and on the small-scale anisotropy of the canopy. For instance, row crops with large open spaces between plants require measurements at a higher level, so that the relevant air properties at a certain horizontal level become homogenous by air mixing, as it rises. Sharma (1985), Monteith and Unsworth (1990), Jensen (1990), Rosenberg et al. (1983) and Jones et al. (1992) describe the general principles and conditions of application of these methods.

Above woody stands, the EC and the Bowen ratio methods are commonly used; aerodynamic methods or derivations are difficult or impossible to apply (Thom et al., 1975; Raupach, 1979), namely because of the very small gradients observed above these stands and the difficulty in finding appropriate functions to account for stability conditions. The Bowen ratio method should be applied with much caution whenever a large part of the radiation reaches the soil, as in many orchards, because the method supposes the same level for sensible and latent heat exchanges. The EC method, first described by Swinbank (1951), is often the only viable alternative. It is based on very fast measurements at one single level of vertical wind speed and either horizontal wind speed, temperature or humidity, according to the flux being measured: momentum, sensible or latent heat flux, respectively (see Baldocchi et al., 1988; Leuning and Moncrieff, 1990 and Kaimal and Finnigan, 1993, among others). Under certain circumstances (slopes, for instance), all components of wind velocity have to be measured in order to perform appropriate axis rotation. Developments of acquisition data systems and sensors in recent years have allowed its use in an increasing number of laboratories, but the accumulated information for woody species is so far limited, especially for long term data series.

### 2.3 Modeling ET

The ET measurements are used primarily for research purposes - for a better understanding of the physical and physiological process involved and for the evaluation of ET models. Evapotranspiration models of woody crops can promote a more efficient use of water at farm level where research methods are difficult to implement due to expensive equipment and specialized know-how. Furthermore, ET models provide estimations based on time-series meteorological data, usable for the statistical analysis necessary for the planning of irrigation infrastructures. As an example, a data set of estimated ET for 30 years can be analysed, using the total annual ET and the ET for the month of maximum consumption, allowing the development of a probability distribution function. According to the selected level of risk, it can be decided the annual amount of water necessary to replace ET and also the peak flow required, respectively in calculating the area to be irrigated and the capacities of water delivery systems.

When looking back to the history of the experimental tools and concepts about ET, we understand why the estimation of the maximum ET of a crop (ETc) has been approached through an empirical equation making use of the ETc of a well irrigated reference crop, the so called reference ET (ETo), and a crop coefficient (Kc), relating the ETc of a certain crop to ETo. An advantage of a reference crop with a value of Q (Equation [1]) as high as possible (traditionally grass or alfalfa) is that its ETc is relatively independent of stomatal behaviour allowing ET estimates based on meteorological variables, for which historical records are available.

Based on this approach, many equations for the estimation of ETo have been developed and used, both empirically or more physically based, according to the available data and to the evolution of the knowledge on ET (references in Section 1). Due to the nature of the process, it is common to use equations based on currently available meteorological data. This ET estimation procedure (ETc = ETo x Kc) has provided good approximations for many applications but the answers are not adequate in all cases. Some of the limitations of this approach can be described as follows.

Firstly, it is well known that crop coefficients are not easily extrapolated because they are dependent upon cultural practices (distance between crop rows, soil cover, irrigation practices, etc.), especially when the crops do not completely cover the soil, as in many irrigated orchards. Allen et al. (1998) present an approach that takes this into account, as an improvement to the values proposed by Doorenbos and Pruitt (1977). However, using different independent methods, values of Kc lower than those suggested were measured in several row crops (Katerji et al., 1990; Ferreira, 1987; Ferreira et al., 1996; Pa?o et al., 2006; Silva et al., 2007).

Secondly, even if Kc is adequate and there is a good estimation of ETc, it is still necessary to solve the problem of calculating ET when the crop is stressed and actual water use (ETa) is below ETc (Figure 1). There is experimental evidence that, in some cases (for instance, in sandy soils), ET from well irrigated crops progressively decreases between irrigations (Itier et al., 1990) with average ETa being considerably less than ETc, as shown in Section 5. This deficiency can be accounted for by the introduction of a stress coefficient, defined as Ks = ETa/ETc, so that ETa = ETo x Kc x Ks. In some cases, a correction for Kc values could be considered, when those values were obtained by methods that did not allow a detailed temporal analysis (soil measurements, drainage lysimeters), as discussed later. Yet, if there is a moderate or intensive water stress due to water restrictions, e.g. for crop quality management or because of water shortage, the corresponding changes in ET are reflected by Ks. A reduction in Ks is mainly related to stomatal closure, expressed by rc. If rc is not available, it can be expressed as a function of other water stress related variables. As mentioned above, a well known example is the discussion by Denmead and Shaw (1962) of the relationships between the relative decrease of T and soil water depletion, expressed as increasingly negative soil water potential.

When estimating ET, a relationship has to be used that implicitly or explicitly includes the stomatal closure relative to stress, if any. Whenever a crop corresponds to low Q coefficients (high and rough stands) the limiting factor for ET is stomatal conductance (if not the radiation input) and, as a consequence, the limitation mentioned above is even more critical. Using the words of Jones (1984), the relative insensitivity of ET to stomatal aperture variations (in low crops) has been extrapolated to inadequate situations.

Using simplistic assumptions, the reduction in ET, expressed as Ks, can be calculated as

Ks = [A + y (1+ rc stress/ra) ] / [(A + y (1+ rc irrig/ra) ]. Figure 3 illustrates how the reduction on ET is relatively more important (lower Ks) for crops that tend to have lower aerodynamic resistances such as forests (same values as in Figure 2, for aerodynamic resistances: 200 to 5).

Figure 3: Stress coefficient in relation to canopy resistance rc, for the same aerodynamic resistances of Figure 2: 200 s/m to 5 s/m, for stands with high to low Q, respectively. The circles suggest that, for a low crop, canopy resistance tends to start from higher values (thin circle) and, for a forest, it eventually starts from lower values (thick circle), as different species can correspond to different ranges of rc

Figure 3: Stress coefficient in relation to canopy resistance rc, for the same aerodynamic resistances of Figure 2: 200 s/m to 5 s/m, for stands with high to low Q, respectively. The circles suggest that, for a low crop, canopy resistance tends to start from higher values (thin circle) and, for a forest, it eventually starts from lower values (thick circle), as different species can correspond to different ranges of rc

Another approach (one-step) is the use of an ET model that directly provides ET estimations. The Penman-Monteith (PM) uni-layer or big-leaf model (Monteith, 1965) includes the stomatal resistance at the canopy level and the environmental variables in one single equation and has become the most used equation for ETa estimations, provided all the variables are known or can be estimated:

ET = [A(Rn-G) + p cp fe-ea) / ra] / [(A+ y (1+ rc/ ra) ] (2a)

where Rn is net radiation, G is the heat flux to the soil, p is air density, cp is the specific heat of air at a constant pressure, ea-ed is the air vapor pressure deficit and the other symbols are defined in Equation [1]. Environmental variables should be measured above the canopy considered. Physical parameters and some of the variables can be calculated according to the equations described - for instance by Burman et al. (1983) and Allen et al. (1986).

The PM equation [2a] can be written in the same form as the Penman (Penman, 1948) equation [2b], replacing y by y', defined according to Monteith (1985) as y'= Y (1+ rc/ra):

Using y', the Q coefficient can be written as:

If rc/ra is low, y' is similar to y, ^ close to 1 (low crops, under no stress) and the ET estimations using Penman or PM equations are similar, if environmental variables measured at the reference level are identical. If rc/ra is high, y' is much higher than y, ^ tends to zero (woody crops, in general, if not wet) and ET estimated with PM equation can be much smaller than the values from Penman equation (other inputs being equal).

One of the obstacles when using these models is to obtain reliable values of ra. Penman (1948) suggested an empirical wind function, for average conditions. Whenever possible, the calculation of ra should consider the conditions of instability during the day because the conductance in highly unstable conditions can increase by an order of magnitude in relation to the conditions of validity of the logarithmic wind profile (Thom and Oliver, 1977; Itier and Katerji, 1983). Furthermore, in literature there is no consistency on whether ra includes the resistance of leaf boundary layers which can vary a lot within complex canopies, either with distance from soil (Ferreira et al., 1994) or due to shelter or directional effects (Daudet et al.,

The stomatal behaviour in uni-layer ET models is expressed by the variable rc (Equations [1], [2] and [4]). It is also called canopy resistance (Reifsnyder et al., 1991). In some cases it is directly derived from measurements with porometers but more often it is estimated using rs models that can be empirical (Jarvis, 1976), semi-empirical as Ball et al. (1987) or modified -i.e. Ball- Berry (Leuning, 1990, 1995; Dewar, 2002) or even hybrid (e.g. Yu, 2004). Even if stomatal behaviour is not completely understood (e. g. revision by Zavala, 2004) some of these models, by integrating at least the effects of plant or soil water status, light intensity and air humidity/temperature, and often CO2 concentration) can provide reasonable estimates. The up-scaling needed to obtain values at the canopy level is a key challenge when based on input variables.

ET is influenced by the aerodynamic and energy (radiation interception) characteristics of the canopy. Both have consequences on rs because the leaves of layers with different environmental conditions have different values of rs. As the relationship between ET and rs is not linear, several multi-layer models have been proposed, in which total ET corresponds to the sum of ET from each one of the single layers sharing the radiation and momentum absorption and contributing differently to the total heat exchanges. The models described by Shuttleworth and Wallace, 1985; Lhomme, 1988a are some of the earlier well known examples. Following the comment by Roberts et al. (1993) it seems better to use multi-layer models whenever important gradients in the canopy are observed. In other conditions (Raupach and Finnigan, 1988; McNaughton and Jarvis, 1991) it seems better to use single-layer models that give very acceptable results, provided representative values of the canopy resistances are used (Lhomme, 1991). It is far more complicated to work with sparse canopies like some Mediterranean agro-forestry systems (montado) or highly anisotropic canopies (as some vineyards or very open orchards).

Remote sensing methodologies, using thermal infrared measurements, have recently been used to assess actual evapotranspiration of agricultural crops (Allen et al., 2007; Johnson et al., 2007; Tasumi and Allen, 2007), forests (e.g., Jones et al., 2004; Leuning et al., 2005), and riparian vegetation (e.g., Nagler et al., 2007), or to integrate different kinds of vegetated surfaces to provide water balance information on a basin scale (Bastiaanssen et al., 2005).Thermal infrared methods can also be applied to the detection of water stress (e.g., Jones at al., 2002; Falkenberg et al., 2007) or as a tool to estimate leaf area index (e.g., Xavier and Vettorazzi, 2004) or canopy cover (e.g., Wang et al., 2007). Either satellite or airborne measurements are usually used, with the latter having the advantage of not being limited to rigid large time intervals. Results of ET estimation from airborne imaging spectrometry for a montado system in Portugal were shown by Jones and Archer (2003).

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