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Penman–Monteith reference evapotranspiration adapted to estimate irrigated tree transpiration
agricultural water management 83 (2006) 153–161
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Penman–Monteith reference evapotranspiration adapted to estimate irrigated tree transpiration Antonio Roberto Pereira a,*, Steve Green b, Nilson Augusto Villa Nova a a b
Departamento de Cieˆncias Exatas, Escola Superior de Agricultura Luiz de Queiroz/USP, Piracicaba, SP 13418-900, Brazil Environment and Risk Management Group, HortResearch Institute, Private Bag 11-030, Palmerston North, New Zealand
article info
abstract
Article history:
The Penman–Monteith equation as parameterized by the FAO-56 bulletin to compute grass
Received 18 March 2005
reference evapotranspiration (E0, L ground m2 d1) was used to predict transpiration of
Received in revised form
irrigated orchard apple trees, olives, grapevines, kiwifruit and an isolated walnut tree. Sap
12 October 2005
flow (S, L plant1 d1) measured by the compensation heat-pulse technique was taken as the
Accepted 15 November 2005
tree transpiration on a daily time scale, and it proved to be a very good way to connect E0
Published on line 10 January 2006
with the individual plant water use. With the exception of the kiwifruit with large nighttime transpiration, results from 102 days from five independent experiments with the other
Keywords: Penman–Monteith
species substantiate the working hypothesis that S = E0AL/2.88, where AL (m2 of leaf plant1) is the plant leaf area, and 2.88 is the hypothetical grass leaf area index. This is an indication
Sap flow
that under well-irrigated conditions transpiration per unit leaf area is very similar regard-
Heat-pulse
less of the plant canopy size or shape. The present scheme eliminates the need of a crop
FAO-56 Crop coefficient
1.
coefficient. Two alternatives for estimating the kiwifruit transpiration are also presented.
Introduction
The problem of predicting water use by plants is very complex and involves the need of measuring many environmental and biological variables. Evapotranspiration is driven by the meteorological conditions but it is also dependent on factors imposed by the plants and by the amount of soil water available to the roots. If soil water is not limiting, the transpiration will be conditioned by the leaf area. When vegetation completely shades the ground, it has been assumed that the transpiring surface is equivalent to the covered ground area, even when the leaf area index differs from unity. However, Doorenbos and Pruitt (1974) have defined reference evapotranspiration as that occurring in an evenly clipped grass field with height between 0.08 and 0.15 m, and in such conditions the hypothetical effective grass leaf area index is 2.88 m2 m2 (Allen et al., 1989, 1998).
# 2005 Elsevier B.V. All rights reserved.
For orchard and isolated plants some attempts have been made to take into account the effective transpiring leaf area. In a hedgerow apple orchard, Thorpe (1978) measured the net radiation absorbed through an imaginary cylindrical surface enclosing part of the row using eight static linear net radiometers. A similar array was used by Smith et al. (1997) enclosing a windbreak canopy. A revolving circular enclosing structure (whirligig) containing eight standard net radiometers was used around isolated trees (McNaughton et al., 1992; Green, 1993), orchard apple trees (Green and McNaughton, 1997; Green et al., 2003b) and olives (Green et al., 2002). A similar structure with six net radiometers was used around an orchard citrus tree (Pereira et al., 2001). These are examples of efforts to effectively consider the energy exchanging leaf surface. Such information was then used in the Penman– Monteith (PM) model (Monteith, 1965) to estimate tree transpiration. The PM model needs auxiliary sub-models or parameterizations for the conductances (Landsberg and
* Corresponding author. E-mail addresses: [email protected] (A.R. Pereira), [email protected] (S. Green), [email protected] (N.A. Villa Nova). 0378-3774/$ – see front matter # 2005 Elsevier B.V. All rights reserved. doi:10.1016/j.agwat.2005.11.004
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agricultural water management 83 (2006) 153–161
Powell, 1973; Jarvis, 1976; Thorpe et al., 1980; McNaughton, 1994; Green and McNaughton, 1997; Villalobos et al., 2000; Rana et al., 2005), but they need local calibrations. An alternative approach less demanding on site specific data and calibration should be sought. Ferna´ndez et al. (2001) and Nicolas et al. (2005) used grass reference evapotranspiration (E0, mm d1), as computed by the PM-FAO-56 scheme (Allen et al., 1998), to estimate the daily sap flow (S, L tree1 d1) of well-irrigated olives and apricot trees. They reported statistical linear relationships between S and E0 given by a nearby weather station, but such empirical relationships are site specific. Hatton et al. (1998) showed a linear relationship between eucalyptus sap flow and the tree leaf area. Combining both approaches it can seen dimensionally that S = E0AL/LG, where AL (m2 tree1) is the tree leaf area, and LG is the grass leaf area index (m2 leaf m2 ground). The working hypothesis is that sap flow per unit canopy leaf area of irrigated orchard trees is equivalent to E0 per unit grass leaf area. E0 is the amount of water used by a hypothetic grass surface with an estimated LG = 2.88 m2 of leaf (Allen et al., 1989, 1994, 1998). It will be shown that such simple approach works well on a daily time scale for most of the irrigated orchard plants without any site specific calibration or sophisticated net radiation measurements.
2.
The Penman–Monteith approach
This section shows the depth of the simplification here proposed for estimating tree transpiration on a daily time scale, avoiding a myriad of assumptions and measurements. It is reviewed some modeling efforts to use the Penman– Monteith equation for orchards and isolated plant conditions.
2.1.
Tree transpiration modeling
The Penman–Monteith approach (Monteith, 1965) is known as the ‘‘big leaf’’ model. Following Jarvis and McNaughton (1986), the Penman–Monteith equation for estimating tree transpiration (T) can be represented as: sRn þ hzrc p Da ga i T¼ h l s þ hg z þ ggas
(1)
where Rn is the net radiation, Da the ambient air vapor pressure deficit, ga the boundary layer conductance, gs the ‘‘big leaf’’ stomatal conductance, g the psychrometric coefficient, r the air density, cp the air specific heat at constant pressure, s the slope of the saturation vapor pressure curve at air temperature, and l is the latent heat of vaporization. The factor h represents the ratio between the boundary layer conductance for water vapor and for sensible heat and its most probable value is 0.93 (Thorpe, 1978; Monteith and Unsworth, 1990; Green, 1993; Caspari et al., 1993), but rounding it to unity (Green and McNaughton, 1997; Villalobos et al., 2000; Green et al., 2003b,c) makes little difference in practical terms because of the many uncertainties introduced in the parameterization of the other variables, as described in the sequence.
The factor z arises from the energy balance of the big leaf, and z = 1 if the leaf has stomata on both sides, z = 2 if the stomata are only in one side. It is a common practice to use z = 2 in the denominator but not in the numerator implicitly incorporating it in ga (Butler, 1976; Thorpe, 1978; Green, 1993; Caspari et al., 1993; Edwards and Warwick, 1984; Green et al., 1989, 2003b,c; Green and McNaughton, 1997; Zhang et al., 1997). Boundary layer conductance (ga, in m s1) can only be estimated and one model frequently used for trees with leaves subjected to mutual interference is that proposed by Landsberg and Powell (1973), that is: ga ¼ 0:0172 p0:56 ðU=DÞ0:5
(2)
with p estimated by the ratio between the tree leaf area and its silhouette area projected onto a vertical plane, D is a characteristic leaf dimension (in m) sometimes taken as the square root of the mean leaf area and U is the average wind speed (in m s1) at the mid-canopy height. Even though this model is almost standard, for olive trees orchard Villalobos et al. (2000) has taken: ga ¼
u2 uz
(3)
as described in Lhomme (1991), where u* is the friction velocity determined by a sonic anemometer and uz is the 10 min average horizontal wind speed measured at a reference height above the trees. For a Clementine citrus orchard Rana et al. (2005) took: ga ¼
k2 u z zd ln zd z0 ln hc d
(4)
where the zero-plane displacement (d), and the roughness length (z0) are fixed proportions of the mean tree height (d = 0.67hc; z0 = 0.1hc), and k is the von Karman constant. Yunusa et al. (2000) used a similar expression given by Thom and Oliver (1977) for estimating regional evapotranspiration. Canopy conductance (gs, in m s1) has been estimated by sampling randomly a very few sunlit and shaded leaves weighted by their corresponding leaf areas throughout the day at fixed intervals (Thorpe, 1978; Green, 1993; Caspari et al., 1993; Green et al., 2003a), with uncertainties of 10–30% (Warrit et al., 1980). Field measurements are labor intensive and cannot be made automatically as the sensor interferes with the leaf creating an artificial environment. Simultaneous measurements in leaves with different exposures are almost impossible with present technology. An alternative is to rely on empirical models (Carlson, 1991) such as those given by Jarvis (1976) and Thorpe et al. (1980). The Jarvis model predicts gs by a maximum conductance gmax multiplied by a series of non-dimensional factors varying from 0 to 1. Results from field experiments with plentiful soil water in the root zone show that gmax varies with and within plant species (Kelliher et al., 1995). The empirical function for each environmental factor varies from linear with a single parameter to non-linear with several coefficients and many examples are available (Winkel and Rambal, 1990; Green and McNaughton, 1997; Zhang et al., 1997; Villalobos et al., 2000; Green et al., 2003b). To simplify this presentation only one Jarvis-type model is here described. In this example,
agricultural water management 83 (2006) 153–161
gs is related to the ambient vapor pressure deficit Da and the photosynthetic photon flux density on the leaf surface Qp as: b1 b2 Qp gs ¼ þ b3 ð1 b4 Da Þ (5) b1 þ b2 Qp with the empirical coefficients interpreted as: b1 is the maximum conductance at full sunlight, b2 the slope of the light response curve approaching zero sunlight, b3 the corresponding conductance in zero sunlight, and b4 expresses the Da effect (Green and McNaughton, 1997; Green et al., 2003b). The Thorpe et al. (1980) model is more restrictive and it is expressed as: ! 1 dDa (6) gs ¼ gmax 1 þ bQp1 where d and b are empirical coefficients (Green et al., 2003c). Eqs. (5) and (6) bring another unknown Qp which has also to be modeled in each orchard condition. According to Green and McNaughton (1997), each unit area of sunlit leaves receive an amount of Qp represented by: Qp ¼
0:8Rp 2 cosðZÞ
(7)
where Rp is the incoming photon flux density expressed on a ground area basis, Z the sun’s zenith angle, and the factor 0.8 accounts for the leaf absorbance. However, Green et al. (2003c) assumed that Qp = 0.5Rp. It was also assumed that shaded leaves receive 0.1Qp. The overall canopy leaf conductance will be a weighed average given by the fraction of sunlit and shaded leaf area. Yunusa et al. (2000) used a linear regression between gs and an index formed by the combination of daily averages of the incoming solar radiation, the specific humidity, and the vapor pressure deficit. Rana et al. (2005) opted for an empirical linear relationship between ga/gs and ga/g* (Katerji and Perrier, 1983), calibrated locally, with the critical conductance g* defined as: g ¼
sgðRn GÞ ðs þ gÞrcp Da
(8)
where G is the flux of heat into the soil and the other terms were defined previously.
2.2.
Calculation approaches
Different approaches have been used to adapt the Penman– Monteith (PM) equation to calculate daily total transpiration of whole trees. In general, hourly or shorter time scale transpiration is calculated and the 24 h total is obtained by accumulation. The scheme for the calculation varies and some of them are now presented. As the canopy is composed by a myriad of leaves one approach is to split proportionally the ‘‘big leaf’’ assuming that a fraction of total leaf area is uniformly sunlit receiving the total canopy net radiation, and the remainder is shaded receiving only diffuse radiant energy and zero net radiation (Green, 1993; Green and McNaughton, 1997; Green et al., 2003b,c). Canopy transpiration is then the summation of the transpiration of the two fractions of leaves throughout the day. Whole canopy net radiation is measured by an array of net radiometers enclosing the tree (whirlgig, McNaughton
155
et al., 1992). Wind speed, air temperature, and vapor pressure deficit are measured at a position near the mid-canopy height. Another approach is to assume that the tree canopy absorbs the same amount of radiation as a horizontal plane area (AP) equivalent to the ground area covered by the projected tree canopy (Caspari et al., 1993). Net radiation measured by a single sensor positioned immediately above the tree is adjusted as RnAP. The vapor pressure deficit term of the PM equation is then multiplied by the total canopy leaf area (AL). Wind speed, air temperature, and vapor pressure deficit are measured at a position near the mid-canopy height. A third approach combines measurements of meteorological elements given by a nearby automatic weather station with measurements of leaf conductance (Edwards and Warwick, 1984; Zhang et al., 1997). For Zhang et al. (1997) net radiation per unit leaf area was taken to be equal to 50% of the grass net radiation, and the result given by Eq. (1) is multiplied by the total canopy leaf area (AL). For Edwards and Warwick (1984) the canopy net radiation is given by the grass net radiation times the canopy leaf area. Rana et al. (2005) used the average of four net radiometers above the orchard. Compared with sap flow measurements the above approaches gave satisfactory results. Edwards and Warwick (1984), Zhang et al. (1997) and Yunusa et al. (2000) results indicate that a less intensive orchard measurements approach can also give reliable estimates. The approach here proposed is to use only measurements of a regional weather station (Ferna´ndez et al., 2001; Nicolas et al., 2005) and the plant canopy leaf area, as described below.
2.3.
FAO grass reference evapotranspiration
As described in Allen et al. (1998), the FAO parameterization scheme to estimate grass reference evapotranspiration (E0, L ground m2 d1) adapted the Penman–Monteith equation to be used with daily total net radiation (Rn, in MJ ground m2 d1) and the corresponding daily averages for the air temperature (Tmean, in 8C), wind speed (U2, in m s1), vapor pressure deficit (Da, in kPa), and conductances. Boundary layer conductance for the grass surface was taken as ga = U2/208 (in m s1). The bulk surface conductance gs was set constant and equal to 1/ 70 m s1, resulting in ga/gs = 0.34U2. Assuming a constant l (=2.45 MJ L1) the PM-FAO equation is then expressed as: E0 ¼
a U2 0:408sRn þ T900gD mean þ273
s þ gð1 þ 0:34U2 Þ
(9)
As E0 given by Eq. (9) is for a hypothetical grass surface with leaf area index (LG) assumed constant and equal to 2.88 m2 m2, then E0 per unit leaf area of the grass is E288 = E0/2.88. It will be shown that such normalized value should be a good estimate of tree canopy transpiration per unit leaf area.
3.
Material and methods
3.1.
Sites and measurements
Six data sets from field experiments in New Zealand were used in this study. One data set came from an experiment at Massey University Research Orchard, near Palmerston North (40.28S,
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were removed and measured by a leaf area meter validating the point-quadrant approach. The trees and vines in the above experiments were instrumented to give the sap flow using the compensation heat-pulse technique (Green and Clothier, 1988; Green et al., 2003a). Daily sap flow per unit canopy leaf area for each tree or vine was calculated and compared with the estimated PM reference evapotranspiration per unit leaf area of the hypothetical grass surface. An automatic weather station was setup above a grass patch near each orchard and the walnut tree to record net radiation, air temperature and humidity, and wind speed. Net radiation was taken at a position well away from any shadows.
175.48E), from 17 to 25 January 1992, with an isolated 10-yearold and 3.5 m high walnut tree with an estimated canopy leaf area of 26.4 m2 during the experiment (Green, 1993). Leaf area was estimated by measuring 10% of the total number of leaves. Two data sets are from experiments with irrigated apple trees (Malus domestic Borkh.) described by Green and McNaughton (1997) and Green et al. (2003b). One experiment was during 10 days of the summer of 1994 and 1995 at Massey with a large 14-year-old apple tree (cv. Splendour/MM 106) with a canopy leaf area of 35.5 m2. The 3.7 m tall tree was in a 3 m 4 m spacing orchard with ground covered by grass except for 1 m wide strip of bare soil close to each tree row. The other data set is from Nelson Research Centre, Motueka (41.68S, 1738E), during 23 days of the summer of 2000 and 2001, with a dwarf apple tree (cv. Braeburn/M.9) with 8.65 m2 of canopy leaf area. The tree spacing was 2 m 2.1 m with 1 m wide strip of bare soil around the tree rows. Canopy leaf area was estimated at the end of each experiment by removing all the leaves and passing a sub-sample through a leaf area meter. One data set is from an experiment in a commercial field at Craggy Range vineyards in Hastings (39.658S, 176.88E) with 5year-old drip irrigated Merlot grapes (Vitis vinifera L.) in a 2 m by 1.5 m spacing on bare stony soil conducted during 42 days of the 2003 and 2004 summer. The grapevine canopy was 1.5 m tall and the leaf area was evaluated every 2 and 3 weeks. Leaf area was measured every other week and for each day it was linearly interpolated between two consecutive measurements. Another data set came from an experiment with drip irrigated 4-year-old olive trees (Olea europaea L. cv. Barnea) carried out on the Ponder Estate (418300 S, 1738520 E) in Marlborough between October 1999 and April 2000 (Green et al., 2002). The trees were planted in rows 6 m apart at a tree spacing of 5 m. Grass covered the ground except for a 2 m wide herbicide strip along each row. Leaf area was estimated to be 13.5 m2 by counting all leaves and removing a fraction (1 in 50) whose area was measured using a leaf area meter. An experiment was carried out at Massey in a perennial kiwifruit vine (Actinidia deliciosa) orchard from 30 January to 24 February 1997. Total leaf area was estimated every 12–14 days by a point-quadrant approach where a sharpened rod was pushed vertically through the canopy volume to record the number of leaf contacts on a 30 cm 30 cm grid underneath the vine. The total leaf area was taken to be equal twice the average leaf contact number multiplied by the groundprojected silhouette of the canopy (3.6 m 3 m) as described in Greer et al. (2004). At the end of the experiment all leaves
3.2.
Computations
The PM-FAO equation (7) was used to estimate E0. Integrated daily grass net radiation was expressed in MJ m2 d1. Soil heat flux was set equal to zero to represent the condition of an isolated tree. As described in Allen et al. (1998), daily average vapor pressure deficit was taken as Da = es ea, where es = 0.5[es{Tmax} + es{Tmin}] and ea = [es{Tmax}RHmin + es{Tmin}RH2 with Tmean = max]/200, and s = 4098es{Tmean}/(237.3 + Tmean) 0.5(Tmax + Tmin). The psychrometric coefficient was set constant and equal to 0.066 kPa 8C1 for all experiments. The FAO-56 parameterization assumes a hypothetic grass surface with a leaf area of 2.88 m2. E0 per unit grass leaf area corresponds to E288 = E0/2.88 (in L m2 of leaf area d1). Graphical and statistical comparisons between measured and estimated daily sap flow were performed. Root mean square error (RMSE) and coefficient of determination (r2) were also computed.
4.
Results and discussion
As suggested by Ferna´ndez et al. (2001) and Nicolas et al. (2005), sap flow (S in L plant1 d1), in isolated and orchard trees, was linearly related to the PM-FAO-56 grass reference evapotranspiration (E0 in mm d1) and Table 1 summarizes the results. Statistical coefficients were site specific and even for the same species (e.g., apples) the function for one orchard could not be used for the other. It is obvious that under the same E0 conditions the sap flow of irrigated trees will be a positive function of the total canopy leaf area, as implied in the Hatton et al. (1998) sap flow-leaf area relationships. Expressing the
Table 1 – Summary of the statistical relationships (Y = a + bX) between integrated daily sap flow (S, in L plantS1 dS1) and the Penman–Monteith grass reference evapotranspiration (E0, in mm dS1) a
b
r2
RMSE
n
S (L plant1 d1)
0.28 0.02 2.85 1.87 1.01 16.41 36.6
3.09 12.28 4.10 8.85 1.30 13.33 24.42
0.8458 0.8762 0.8555 0.9740 0.5820 0.8492 0.6241
1.39 4.87 2.75 1.63 4.87 6.16 –
23 10 31 8 30 26 59
1.3–13.6 13.4–56.1 6.7–32.9 14.8–39.6 0.8–56.1 28.9–78.6 40–100
Crop Apples dwarf Apples normal Olives Walnut Grapevines Kiwifruit Apricota a
Source: Nicolas et al. (2005).
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Table 2 – Summary of the statistical relationships (Y = a + bX) between integrated daily sap flow per unit leaf area (SA, in L mS2 leafS1 dS1) and the Penman–Monteith grass reference evapotranspiration (E0, in mm dS1) Crop Apples dwarf Apples normal Olives Walnut Grapevines Kiwifruit
a
b
r2
RMSE
n
AL
0 0 0 0 0.47 0.35
0.346 0.346 0.348 0.356 0.195 0.420
0.8450 0.8762 0.8348 0.9698 0.5109 0.8628
0.157 0.129 0.214 0.062 0.182 0.183
23 10 31 8 30 26
8.65 35.5 13.5 26.4 2.76–5.83 32–36.7
AL is the canopy leaf area (in m2).
sap flow per unit leaf area (SA, in L m2 leaf d1) eliminates the effect of canopy size, and the statistical analysis resulted in very similar relationships for most of the orchards (Table 2). For apples (dwarf and normal sizes), olives and walnut trees the y-intercept did not differ statistically from zero and the regression lines were forced through the origin. Pooling the corresponding data seta resulted in the overall regression line SA = 0.348E0 (r2 = 0.8851, n = 72, RMSE = 0.172 L m2 leaf d1). Grapevines and kiwifruit data did not follow this regression, but forcing the regressions also through the origin (for the sake of comparisons) resulted in b = 0.355 for the grapevines, and b = 0.522 for the kiwifruit vines. Discarding the kiwifruit data set from the analysis the weighed average for the regression coefficient was b = 0.349. This empirical function indicates that tree sap flow per unit canopy leaf area corresponds, on average, to 35% of E0. It can be a mere coincidence but b = 0.349 is very close to the inverse of the hypothetical leaf area of the reference grass surface, i.e., 2.881 = 0.347. The statistical results indicate that, on a leaf area basis, tree sap flow does not differ from E0/2.88 (=E288). This is an indication that transpiration on a leaf area basis is very similar regardless of the plant canopy size and shape for most of the plants. Normalizing both flows on a unit leaf area basis reduced the range of the variables to a common interval allowing a better graphical view and comparisons of the dispersion points (Fig. 1). The maximum measured SA was about 2.5 L m2 of leaf d1. Pooling the data for the grapevines, the walnut, the two apple trees (normal and dwarf sizes), and the olives tree the statistical relationship did not differ from
the perfect fit line, that is, SA = 1.01E288 (r2 = 0.8301, n = 102, RMSE = 0.19 L m2 of leaf area d1). However, for the kiwifruit vine transpiration there was a large underestimation of 50%, on average (SA = 1.502 E288; r2 = 0.8065, n = 26), and this special case will be discussed below. As the daily sap flow (S) is equal to SA times the canopy leaf area (AL) and the intention is to predict water use on a daily time scale (Fig. 2), the statistical relationships found between the integrated daily sap flow and the estimated transpiration (E288AL) for each orchard condition is summarized in Table 3. For the walnut, apples, olives and grapevines the slope (b) of the regression lines did not differ statistically from the equal values line (1:1). The daily accumulated sap flow for the walnut tree (26.4 m2 leaf canopy) varied from 14.8 to 39.6 L tree1 d1, and the comparison with the estimated transpiration gave the following statistical relationship: S = 1.026E288AL (r2 = 0.9698, RMSE = 1.63 L tree1 d1, n = 8). RMSE represented about 6% of the average sap flow. For the sake of comparison, using the same data set, the more complex and data intensive scheme used by Green (1993, his Table 1) with computations every 20 min during the day to predict the walnut daily total sap flow (W, L tree1 d1) resulted in S = 1.107W (r2 = 0.8829; n = 9), that is, an under estimation of 10%. The measured sap flow accumulated during the 8 days amounted to 231.6 L, the estimated transpiration added up to 224.5 L with the present scheme, and it summed up to 209.4 L with the Green (1993) short time computations. Surprisingly, the much less intensive approach here proposed gave a better estimate of the daily sap flow.
Fig. 1 – Modified Penman–Monteith FAO-56 evapotranspiration (E288) vs. measured sap flow per unit leaf area of irrigated orchard plants. Inside the parenthesis is the number of days for each case.
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Fig. 2 – Measured vs. estimated total daily sap flow for irrigated orchard apples and olivestrees, grapevines and an isolated walnut tree.
For the apple trees the daily total sap flow and the estimated transpiration had the following statistical fit: S = 0.997E288AL (r2 = 0.9456, RMSE = 2.69 L tree1 d1, n = 33). Sap flow varied from 1.3 to 13.6 L tree1 d1 for the dwarf tree (8.65 m2 of leaf area), and from 13.4 to 56.1 L tree1 d1 for the large tree (35.5 m2 of canopy leaf area). RMSE was about 15% of the average sap flow. During 33 days the sap flow accumulated to 604.7 L and the corresponding estimated transpiration was 607.6 L. Estimated tree transpiration (G, L tree1 d1) given by the more complex computational scheme with the same data set and presented by Green and McNaughton (1997) and Green et al. (2003b) resulted in under estimation of about 9%, or S = 1.09G (r2 = 0.9908, n = 33), and it amounted to 539.8 L (12% difference). Olive tree with 13.5 m2 of leaf canopy had a daily sap flow between 6.7 and 32.9 L tree1 d1. Sap flow versus estimated transpiration did not differ statistically from the perfect fit line, that is, S = 1.003E288AL (r2 = 0.8349, RMSE = 2.54 L tree1 d1, n = 31). RMSE was close to 13% of the average sap flow. Sap flow accumulated to 621.7 L and the corresponding estimated transpiration was 609.2 L. Again, the daily integrated transpiration (O, L tree1 d1) given by the more intensive computational scheme of Green et al. (2002) resulted in S = 1.098O (r2 = 0.8560, n = 31), and the estimated water use during the experiment was 551.3 L (11% difference). Comparisons of the daily accumulated sap flow for the grapevines orchard resulted in S = 0.969E288AL (r2 = 0.5109,
Table 3 – Summary of the statistical relationships (Y = bX) between integrated daily sap flow (S, in L plantS1 dS1) and the estimated transpiration (E288AL, in L plantS1 dS1) Crop Apple trees Grapevines Olives Walnut All crops
b
r2
0.997 0.969 1.003 1.026 1.002
0.9456 0.5109 0.8349 0.9698 0.9679
RMSE 2.69 0.94 2.54 1.63 2.00
S average 18.32 4.51 20.06 28.95 15.62
n 33 30 31 8 102
RMSE = 0.94 L vine1 d1, n = 30) with a much smaller S range (0.8–7.2 L vine1 d1) than for the apples, walnut and olive trees. RMSE represented 20% of the average sap flow. During the experiment the leaf area per vine varied from 5.49 m2 at the beginning to 5.83 m2 a week later, and thereafter it decreased to 2.76 m2 after 35 days. Between two measurements the leaf area was linearly interpolated for the daily calculations. Accumulated sap flow during the experiment was 135.3 L, and the estimated water use added up to 131.5 L. No short-term computations are available for comparison. In regard to the kiwifruit, the 24 h integrated sap flow varied from 28.9 to 78.6 L vine1 d1. Vine leaf area increased from 32 m2, at the beginning of the experiment, to 36.9 m2 after 25 days. The large sap flow underestimation shown in Fig. 1 was caused by the large nighttime transpiration (sunset to sunrise) due to incomplete stomata closure (Judd et al., 1986). Nighttime transpiration is here defined as that occurring during the period of negative net radiation. Water use during the night varied from 2.8 to 21.7 L vine1 d1 and it represented about 26% of the daytime transpiration (ranged from 8 to 57%). Such large values are very similar to those reported by Judd et al. (1986) and Green et al. (1989), also in New Zealand orchards. As before, nighttime sap flow (SN, in L vine1 night1) was positively associated with the nighttime atmospheric vapor pressure deficit (DN, in kPa) and such linear regression relationship (SN = 44.488DN, r2 = 0.9097, n = 25) is displayed in Fig. 3. This regression line also accommodates the results described by Green et al. (1989) and not included in the regression. In a humid coastal climate, with rapid onset of dewfall after sunset, nighttime water use was not detected in a windbreak sheltered kiwifruit orchard (McAneney et al., 1992). There are two possible ways to adjust the predicted sap flow for the kiwifruit vines through the approach here proposed. Analysis of the results shown in Fig. 1 indicate an average difference of 0.5 L m2 of leaf d1 between SA and E288, that is, SA (E288 + 0.5). Fig. 4 shows that indeed the daily integrated sap flow was better estimated this way as the points dispersed around the perfect fit line (S = 1.002[E288 + 0.5]AL, r2 = 0.8474; RMSE = 6.07 L vine1 d1, n = 26).
agricultural water management 83 (2006) 153–161
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Fig. 3 – Nighttime sap flow in a kiwifruit vine as a function of the atmospheric vapor deficit during the same period. Results from Green et al. (1989) is shown but not included in the regression.
Fig. 4 – Comparison between the modified Penman– Monteith FAO-56 daily evapotranspiration and the measured sap flow in a kiwifruit vine.
The alternative approach is to add the nighttime sap flow relationship with the vapor pressure deficit, as described in Fig. 3, to the original proposal. In other words, the alternative model is [E288AL + 45DN]. Such approach reduced the under prediction to 9%, on average, or S = 1.09[E288AL + 45DN], r2 = 0.7975; n = 26). In order to have an even dispersion around the 1:1 line, it was found that the second term should go to 60DN. This alternative approach should be preferred as the additional term (SN) vanishes under conditions of nighttime atmospheric vapor pressure saturation (DN = 0). For the sake of comparison, for the same data set, the more complex and more detailed short time scheme with computations for every 30 min throughout the day to predict the 24 h kiwifruit sap flow (K, L vine1 d1) resulted in the following statistical relationship, S = 1.234K (r2 = 0.7957, n = 26). Even though this more intensive data and computational scheme predicts also nighttime transpiration (Green et al., 1989) the under prediction was still large. It is evident that kiwifruit transpiration needs further modeling efforts.
to establish the connection between the reference evapotranspiration and the individual plant water use. The working hypothesis proved valid for canopies with different sizes and exposure to the environment with sap flow varying from 0.8 to 56.1 L plant1 d1, and canopy leaf area from 2.76 to 35.5 m2. In order to become operational it needs an easy way to estimate remotely the tree leaf area throughout the season and many methods are available (Lang and Xiang, 1986; Villalobos et al., 1995; Wu¨nsche and Lakso, 1998; Broadhead et al., 2003; Jonckheere et al., 2004). The present approach eliminates the need of the traditional crop coefficient scheme. As an exception case, it was found that the proposed approach grossly under estimates the kiwifruit sap flow as the leaves continue to transpire at a high rate under nighttime advective conditions. Grass reference evapotranspiration was not able to mimic kiwifruit sap flow under conditions of large nighttime vapor pressure deficits and large nighttime water use. Further adaptation is needed to account for such unusual feature.
5.
Acknowledgement
Conclusions
Results from 102 days of five independent experiments with apples (dwarf and normal sizes), olives and walnut trees and grapevines of different canopy sizes and shapes indicate that, on a daily time scale, the well irrigated canopy transpiration can reliably be estimated through the use of the conventional grass reference evapotranspiration parameterized by the FAO56 bulletin (Allen et al., 1998), with input variables measured at nearby weather stations. Computed reference evapotranspiration is then corrected only by the ratio between the canopy leaf area and the 2.88 m2 of leaf area assumed for the hypothetical reference grass surface. No other empirical correction or adjustment factor was necessary. A remarkably good relationship was found between the estimates and the sap flow determined by compensation heatpulse technique. Integrated daily sap flow was a very good way
This work was partially supported by the Brazilian National Research Council (CNPq).
references
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Judd, M.J., McAneney, K.J., Trought, M.C.T., 1986. Water use by sheltered kiwifruit under advective conditions. NZ J. Agric. Res. 29, 83–92. Katerji, N., Perrier, A., 1983. Mode´lisation de l’evapotranspiration re´elle d’une parcelle de Lucerne: role d’un coefficient culturalle. Agronomie 3 (6), 513–524. Kelliher, F.M., Leuning, R., Raupach, M.R., Schulze, E.D., 1995. Maximum conductances for evaporation from vegetation types. Agric. For. Meteorol. 73, 1–16. Landsberg, J.J., Powell, D.B.B., 1973. Surface exchange characteristics of leaves subject to mutual interference. Agric. Meteorol. 13, 169–184. Lang, A.R.G., Xiang, Y., 1986. Estimation of leaf area index from transmission of direct sunlight in discontinuous canopies. Agric. For. Meteorol. 37, 229–243. Lhomme, J.P., 1991. The concept of canopy resistance: historical survey and comparison of different approaches. Agric. For. Meterol. 54, 227–240. McAneney, K.J., Prendergast, P.T., Judd, M.J., Green, A.E., 1992. Observations of equilibrium evaporation from a windbreaksheltered kiwifruit orchard. Agric. For. Meterol. 57, 253–264. McNaughton, K.G., 1994. Effective stomatal and boundary-layer resistances of heterogeneous surfaces. Plant Cell Environ. 17, 1061–1068. McNaughton, K.G., Green, S.R., Black, T.A., Tynam, B.R., Edwards, W.R.N., 1992. Direct measurement of net radiation and photosynthetically active radiation absorbed by a single tree. Agric. For. Meteorol. 62, 87–107. Monteith, J.L., 1965. Evaporation and environment: the state and movement of water in living organisms. Symp. Soc. Exp. Biol. 19, 205–234. Monteith, J.L., Unsworth, M.H., 1990. Principles of Environmental Physics, 2nd ed. Edward Arnold, London, p. 291. Nicolas, E., Torrecillas, A., Ortun˜o, M.F., Domingo, R., Alarco´n, J.J., 2005. Evaluation of transpiration in adult apricot trees from sap flow measurements. Agric. Water Manage. 72, 131–145. Pereira, A.R., Angelocci, L.R., Villa Nova, N.A., Sentelhas, P.C., 2001. Estimating single tree net radiation using grass net radiation and tree leaf area. Rev. Brasi. Agrometeorol. 9, 187–192. Rana, G., Katerji, N., Lorenzi, F., 2005. Measurement and modeling of evapotranspiration of irrigated citrus orchard under Mediterranean conditions. Agric. For. Meteorol. 128, 199–209. Smith, D.M., Jarvis, P.G., Odongo, J.C.W., 1997. Energy budgets of windbreak canopies in the Sahel. Agric. For. Meteorol. 86, 33–49. Thom, A.S., Oliver, H.R., 1977. On Penman’s equation for estimating regional evaporation. Q. J. R. Meteorol. Soc. 103, 345–357. Thorpe, M.R., 1978. Net radiation and transpiration of apple trees in rows. Agric. Meteorol. 19, 41–57. Thorpe, M.R., Warrit, B., Landsberg, J.J., 1980. Responses of apple leaf stomata: a model for single leaves and a whole canopy. Plant Cell Environ. 3, 23–27. Villalobos, F.J., Orgaz, F., Mateos, L., 1995. Non-destructive measurement of leaf a´rea in olive (Olea europea L.) trees using a gap inversion method. Agric. For. Meteorol. 73, 29–42. Villalobos, F.J., Orgaz, F., Testi, L., Fereres, E., 2000. Measurement and modeling of evapotranspiration of olive (Olea europaea L.) orchards. Eur. J. Agron. 13, 155–163. Warrit, B., Landsberg, J.J., Thorpe, M.R., 1980. Responses of apple leaf stomata to environmental factors. Plant Cell Environ. 3, 13–22.
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comparison of the heat-pulse technique with gravimetric and micrometeorological methods. Irrig. Sci. 20, 1–8. Zhang, H., Simmonds, L.P., Morison, J.I.L., Payne, D., 1997. Estimation of transpiration by single trees: comparison of sap flow measurements with a combination equation. Agric. For. Meteorol. 87, 155–169.
161
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"
Penman–Monteith reference evapotranspiration adapted to estimate irrigated tree transpiration Antonio Roberto Pereira a,*, Steve Green b, Nilson Augusto Villa Nova a a b
Departamento de Cieˆncias Exatas, Escola Superior de Agricultura Luiz de Queiroz/USP, Piracicaba, SP 13418-900, Brazil Environment and Risk Management Group, HortResearch Institute, Private Bag 11-030, Palmerston North, New Zealand
article info
abstract
Article history:
The Penman–Monteith equation as parameterized by the FAO-56 bulletin to compute grass
Received 18 March 2005
reference evapotranspiration (E0, L ground m2 d1) was used to predict transpiration of
Received in revised form
irrigated orchard apple trees, olives, grapevines, kiwifruit and an isolated walnut tree. Sap
12 October 2005
flow (S, L plant1 d1) measured by the compensation heat-pulse technique was taken as the
Accepted 15 November 2005
tree transpiration on a daily time scale, and it proved to be a very good way to connect E0
Published on line 10 January 2006
with the individual plant water use. With the exception of the kiwifruit with large nighttime transpiration, results from 102 days from five independent experiments with the other
Keywords: Penman–Monteith
species substantiate the working hypothesis that S = E0AL/2.88, where AL (m2 of leaf plant1) is the plant leaf area, and 2.88 is the hypothetical grass leaf area index. This is an indication
Sap flow
that under well-irrigated conditions transpiration per unit leaf area is very similar regard-
Heat-pulse
less of the plant canopy size or shape. The present scheme eliminates the need of a crop
FAO-56 Crop coefficient
1.
coefficient. Two alternatives for estimating the kiwifruit transpiration are also presented.
Introduction
The problem of predicting water use by plants is very complex and involves the need of measuring many environmental and biological variables. Evapotranspiration is driven by the meteorological conditions but it is also dependent on factors imposed by the plants and by the amount of soil water available to the roots. If soil water is not limiting, the transpiration will be conditioned by the leaf area. When vegetation completely shades the ground, it has been assumed that the transpiring surface is equivalent to the covered ground area, even when the leaf area index differs from unity. However, Doorenbos and Pruitt (1974) have defined reference evapotranspiration as that occurring in an evenly clipped grass field with height between 0.08 and 0.15 m, and in such conditions the hypothetical effective grass leaf area index is 2.88 m2 m2 (Allen et al., 1989, 1998).
# 2005 Elsevier B.V. All rights reserved.
For orchard and isolated plants some attempts have been made to take into account the effective transpiring leaf area. In a hedgerow apple orchard, Thorpe (1978) measured the net radiation absorbed through an imaginary cylindrical surface enclosing part of the row using eight static linear net radiometers. A similar array was used by Smith et al. (1997) enclosing a windbreak canopy. A revolving circular enclosing structure (whirligig) containing eight standard net radiometers was used around isolated trees (McNaughton et al., 1992; Green, 1993), orchard apple trees (Green and McNaughton, 1997; Green et al., 2003b) and olives (Green et al., 2002). A similar structure with six net radiometers was used around an orchard citrus tree (Pereira et al., 2001). These are examples of efforts to effectively consider the energy exchanging leaf surface. Such information was then used in the Penman– Monteith (PM) model (Monteith, 1965) to estimate tree transpiration. The PM model needs auxiliary sub-models or parameterizations for the conductances (Landsberg and
* Corresponding author. E-mail addresses: [email protected] (A.R. Pereira), [email protected] (S. Green), [email protected] (N.A. Villa Nova). 0378-3774/$ – see front matter # 2005 Elsevier B.V. All rights reserved. doi:10.1016/j.agwat.2005.11.004
154
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Powell, 1973; Jarvis, 1976; Thorpe et al., 1980; McNaughton, 1994; Green and McNaughton, 1997; Villalobos et al., 2000; Rana et al., 2005), but they need local calibrations. An alternative approach less demanding on site specific data and calibration should be sought. Ferna´ndez et al. (2001) and Nicolas et al. (2005) used grass reference evapotranspiration (E0, mm d1), as computed by the PM-FAO-56 scheme (Allen et al., 1998), to estimate the daily sap flow (S, L tree1 d1) of well-irrigated olives and apricot trees. They reported statistical linear relationships between S and E0 given by a nearby weather station, but such empirical relationships are site specific. Hatton et al. (1998) showed a linear relationship between eucalyptus sap flow and the tree leaf area. Combining both approaches it can seen dimensionally that S = E0AL/LG, where AL (m2 tree1) is the tree leaf area, and LG is the grass leaf area index (m2 leaf m2 ground). The working hypothesis is that sap flow per unit canopy leaf area of irrigated orchard trees is equivalent to E0 per unit grass leaf area. E0 is the amount of water used by a hypothetic grass surface with an estimated LG = 2.88 m2 of leaf (Allen et al., 1989, 1994, 1998). It will be shown that such simple approach works well on a daily time scale for most of the irrigated orchard plants without any site specific calibration or sophisticated net radiation measurements.
2.
The Penman–Monteith approach
This section shows the depth of the simplification here proposed for estimating tree transpiration on a daily time scale, avoiding a myriad of assumptions and measurements. It is reviewed some modeling efforts to use the Penman– Monteith equation for orchards and isolated plant conditions.
2.1.
Tree transpiration modeling
The Penman–Monteith approach (Monteith, 1965) is known as the ‘‘big leaf’’ model. Following Jarvis and McNaughton (1986), the Penman–Monteith equation for estimating tree transpiration (T) can be represented as: sRn þ hzrc p Da ga i T¼ h l s þ hg z þ ggas
(1)
where Rn is the net radiation, Da the ambient air vapor pressure deficit, ga the boundary layer conductance, gs the ‘‘big leaf’’ stomatal conductance, g the psychrometric coefficient, r the air density, cp the air specific heat at constant pressure, s the slope of the saturation vapor pressure curve at air temperature, and l is the latent heat of vaporization. The factor h represents the ratio between the boundary layer conductance for water vapor and for sensible heat and its most probable value is 0.93 (Thorpe, 1978; Monteith and Unsworth, 1990; Green, 1993; Caspari et al., 1993), but rounding it to unity (Green and McNaughton, 1997; Villalobos et al., 2000; Green et al., 2003b,c) makes little difference in practical terms because of the many uncertainties introduced in the parameterization of the other variables, as described in the sequence.
The factor z arises from the energy balance of the big leaf, and z = 1 if the leaf has stomata on both sides, z = 2 if the stomata are only in one side. It is a common practice to use z = 2 in the denominator but not in the numerator implicitly incorporating it in ga (Butler, 1976; Thorpe, 1978; Green, 1993; Caspari et al., 1993; Edwards and Warwick, 1984; Green et al., 1989, 2003b,c; Green and McNaughton, 1997; Zhang et al., 1997). Boundary layer conductance (ga, in m s1) can only be estimated and one model frequently used for trees with leaves subjected to mutual interference is that proposed by Landsberg and Powell (1973), that is: ga ¼ 0:0172 p0:56 ðU=DÞ0:5
(2)
with p estimated by the ratio between the tree leaf area and its silhouette area projected onto a vertical plane, D is a characteristic leaf dimension (in m) sometimes taken as the square root of the mean leaf area and U is the average wind speed (in m s1) at the mid-canopy height. Even though this model is almost standard, for olive trees orchard Villalobos et al. (2000) has taken: ga ¼
u2 uz
(3)
as described in Lhomme (1991), where u* is the friction velocity determined by a sonic anemometer and uz is the 10 min average horizontal wind speed measured at a reference height above the trees. For a Clementine citrus orchard Rana et al. (2005) took: ga ¼
k2 u z zd ln zd z0 ln hc d
(4)
where the zero-plane displacement (d), and the roughness length (z0) are fixed proportions of the mean tree height (d = 0.67hc; z0 = 0.1hc), and k is the von Karman constant. Yunusa et al. (2000) used a similar expression given by Thom and Oliver (1977) for estimating regional evapotranspiration. Canopy conductance (gs, in m s1) has been estimated by sampling randomly a very few sunlit and shaded leaves weighted by their corresponding leaf areas throughout the day at fixed intervals (Thorpe, 1978; Green, 1993; Caspari et al., 1993; Green et al., 2003a), with uncertainties of 10–30% (Warrit et al., 1980). Field measurements are labor intensive and cannot be made automatically as the sensor interferes with the leaf creating an artificial environment. Simultaneous measurements in leaves with different exposures are almost impossible with present technology. An alternative is to rely on empirical models (Carlson, 1991) such as those given by Jarvis (1976) and Thorpe et al. (1980). The Jarvis model predicts gs by a maximum conductance gmax multiplied by a series of non-dimensional factors varying from 0 to 1. Results from field experiments with plentiful soil water in the root zone show that gmax varies with and within plant species (Kelliher et al., 1995). The empirical function for each environmental factor varies from linear with a single parameter to non-linear with several coefficients and many examples are available (Winkel and Rambal, 1990; Green and McNaughton, 1997; Zhang et al., 1997; Villalobos et al., 2000; Green et al., 2003b). To simplify this presentation only one Jarvis-type model is here described. In this example,
agricultural water management 83 (2006) 153–161
gs is related to the ambient vapor pressure deficit Da and the photosynthetic photon flux density on the leaf surface Qp as: b1 b2 Qp gs ¼ þ b3 ð1 b4 Da Þ (5) b1 þ b2 Qp with the empirical coefficients interpreted as: b1 is the maximum conductance at full sunlight, b2 the slope of the light response curve approaching zero sunlight, b3 the corresponding conductance in zero sunlight, and b4 expresses the Da effect (Green and McNaughton, 1997; Green et al., 2003b). The Thorpe et al. (1980) model is more restrictive and it is expressed as: ! 1 dDa (6) gs ¼ gmax 1 þ bQp1 where d and b are empirical coefficients (Green et al., 2003c). Eqs. (5) and (6) bring another unknown Qp which has also to be modeled in each orchard condition. According to Green and McNaughton (1997), each unit area of sunlit leaves receive an amount of Qp represented by: Qp ¼
0:8Rp 2 cosðZÞ
(7)
where Rp is the incoming photon flux density expressed on a ground area basis, Z the sun’s zenith angle, and the factor 0.8 accounts for the leaf absorbance. However, Green et al. (2003c) assumed that Qp = 0.5Rp. It was also assumed that shaded leaves receive 0.1Qp. The overall canopy leaf conductance will be a weighed average given by the fraction of sunlit and shaded leaf area. Yunusa et al. (2000) used a linear regression between gs and an index formed by the combination of daily averages of the incoming solar radiation, the specific humidity, and the vapor pressure deficit. Rana et al. (2005) opted for an empirical linear relationship between ga/gs and ga/g* (Katerji and Perrier, 1983), calibrated locally, with the critical conductance g* defined as: g ¼
sgðRn GÞ ðs þ gÞrcp Da
(8)
where G is the flux of heat into the soil and the other terms were defined previously.
2.2.
Calculation approaches
Different approaches have been used to adapt the Penman– Monteith (PM) equation to calculate daily total transpiration of whole trees. In general, hourly or shorter time scale transpiration is calculated and the 24 h total is obtained by accumulation. The scheme for the calculation varies and some of them are now presented. As the canopy is composed by a myriad of leaves one approach is to split proportionally the ‘‘big leaf’’ assuming that a fraction of total leaf area is uniformly sunlit receiving the total canopy net radiation, and the remainder is shaded receiving only diffuse radiant energy and zero net radiation (Green, 1993; Green and McNaughton, 1997; Green et al., 2003b,c). Canopy transpiration is then the summation of the transpiration of the two fractions of leaves throughout the day. Whole canopy net radiation is measured by an array of net radiometers enclosing the tree (whirlgig, McNaughton
155
et al., 1992). Wind speed, air temperature, and vapor pressure deficit are measured at a position near the mid-canopy height. Another approach is to assume that the tree canopy absorbs the same amount of radiation as a horizontal plane area (AP) equivalent to the ground area covered by the projected tree canopy (Caspari et al., 1993). Net radiation measured by a single sensor positioned immediately above the tree is adjusted as RnAP. The vapor pressure deficit term of the PM equation is then multiplied by the total canopy leaf area (AL). Wind speed, air temperature, and vapor pressure deficit are measured at a position near the mid-canopy height. A third approach combines measurements of meteorological elements given by a nearby automatic weather station with measurements of leaf conductance (Edwards and Warwick, 1984; Zhang et al., 1997). For Zhang et al. (1997) net radiation per unit leaf area was taken to be equal to 50% of the grass net radiation, and the result given by Eq. (1) is multiplied by the total canopy leaf area (AL). For Edwards and Warwick (1984) the canopy net radiation is given by the grass net radiation times the canopy leaf area. Rana et al. (2005) used the average of four net radiometers above the orchard. Compared with sap flow measurements the above approaches gave satisfactory results. Edwards and Warwick (1984), Zhang et al. (1997) and Yunusa et al. (2000) results indicate that a less intensive orchard measurements approach can also give reliable estimates. The approach here proposed is to use only measurements of a regional weather station (Ferna´ndez et al., 2001; Nicolas et al., 2005) and the plant canopy leaf area, as described below.
2.3.
FAO grass reference evapotranspiration
As described in Allen et al. (1998), the FAO parameterization scheme to estimate grass reference evapotranspiration (E0, L ground m2 d1) adapted the Penman–Monteith equation to be used with daily total net radiation (Rn, in MJ ground m2 d1) and the corresponding daily averages for the air temperature (Tmean, in 8C), wind speed (U2, in m s1), vapor pressure deficit (Da, in kPa), and conductances. Boundary layer conductance for the grass surface was taken as ga = U2/208 (in m s1). The bulk surface conductance gs was set constant and equal to 1/ 70 m s1, resulting in ga/gs = 0.34U2. Assuming a constant l (=2.45 MJ L1) the PM-FAO equation is then expressed as: E0 ¼
a U2 0:408sRn þ T900gD mean þ273
s þ gð1 þ 0:34U2 Þ
(9)
As E0 given by Eq. (9) is for a hypothetical grass surface with leaf area index (LG) assumed constant and equal to 2.88 m2 m2, then E0 per unit leaf area of the grass is E288 = E0/2.88. It will be shown that such normalized value should be a good estimate of tree canopy transpiration per unit leaf area.
3.
Material and methods
3.1.
Sites and measurements
Six data sets from field experiments in New Zealand were used in this study. One data set came from an experiment at Massey University Research Orchard, near Palmerston North (40.28S,
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agricultural water management 83 (2006) 153–161
were removed and measured by a leaf area meter validating the point-quadrant approach. The trees and vines in the above experiments were instrumented to give the sap flow using the compensation heat-pulse technique (Green and Clothier, 1988; Green et al., 2003a). Daily sap flow per unit canopy leaf area for each tree or vine was calculated and compared with the estimated PM reference evapotranspiration per unit leaf area of the hypothetical grass surface. An automatic weather station was setup above a grass patch near each orchard and the walnut tree to record net radiation, air temperature and humidity, and wind speed. Net radiation was taken at a position well away from any shadows.
175.48E), from 17 to 25 January 1992, with an isolated 10-yearold and 3.5 m high walnut tree with an estimated canopy leaf area of 26.4 m2 during the experiment (Green, 1993). Leaf area was estimated by measuring 10% of the total number of leaves. Two data sets are from experiments with irrigated apple trees (Malus domestic Borkh.) described by Green and McNaughton (1997) and Green et al. (2003b). One experiment was during 10 days of the summer of 1994 and 1995 at Massey with a large 14-year-old apple tree (cv. Splendour/MM 106) with a canopy leaf area of 35.5 m2. The 3.7 m tall tree was in a 3 m 4 m spacing orchard with ground covered by grass except for 1 m wide strip of bare soil close to each tree row. The other data set is from Nelson Research Centre, Motueka (41.68S, 1738E), during 23 days of the summer of 2000 and 2001, with a dwarf apple tree (cv. Braeburn/M.9) with 8.65 m2 of canopy leaf area. The tree spacing was 2 m 2.1 m with 1 m wide strip of bare soil around the tree rows. Canopy leaf area was estimated at the end of each experiment by removing all the leaves and passing a sub-sample through a leaf area meter. One data set is from an experiment in a commercial field at Craggy Range vineyards in Hastings (39.658S, 176.88E) with 5year-old drip irrigated Merlot grapes (Vitis vinifera L.) in a 2 m by 1.5 m spacing on bare stony soil conducted during 42 days of the 2003 and 2004 summer. The grapevine canopy was 1.5 m tall and the leaf area was evaluated every 2 and 3 weeks. Leaf area was measured every other week and for each day it was linearly interpolated between two consecutive measurements. Another data set came from an experiment with drip irrigated 4-year-old olive trees (Olea europaea L. cv. Barnea) carried out on the Ponder Estate (418300 S, 1738520 E) in Marlborough between October 1999 and April 2000 (Green et al., 2002). The trees were planted in rows 6 m apart at a tree spacing of 5 m. Grass covered the ground except for a 2 m wide herbicide strip along each row. Leaf area was estimated to be 13.5 m2 by counting all leaves and removing a fraction (1 in 50) whose area was measured using a leaf area meter. An experiment was carried out at Massey in a perennial kiwifruit vine (Actinidia deliciosa) orchard from 30 January to 24 February 1997. Total leaf area was estimated every 12–14 days by a point-quadrant approach where a sharpened rod was pushed vertically through the canopy volume to record the number of leaf contacts on a 30 cm 30 cm grid underneath the vine. The total leaf area was taken to be equal twice the average leaf contact number multiplied by the groundprojected silhouette of the canopy (3.6 m 3 m) as described in Greer et al. (2004). At the end of the experiment all leaves
3.2.
Computations
The PM-FAO equation (7) was used to estimate E0. Integrated daily grass net radiation was expressed in MJ m2 d1. Soil heat flux was set equal to zero to represent the condition of an isolated tree. As described in Allen et al. (1998), daily average vapor pressure deficit was taken as Da = es ea, where es = 0.5[es{Tmax} + es{Tmin}] and ea = [es{Tmax}RHmin + es{Tmin}RH2 with Tmean = max]/200, and s = 4098es{Tmean}/(237.3 + Tmean) 0.5(Tmax + Tmin). The psychrometric coefficient was set constant and equal to 0.066 kPa 8C1 for all experiments. The FAO-56 parameterization assumes a hypothetic grass surface with a leaf area of 2.88 m2. E0 per unit grass leaf area corresponds to E288 = E0/2.88 (in L m2 of leaf area d1). Graphical and statistical comparisons between measured and estimated daily sap flow were performed. Root mean square error (RMSE) and coefficient of determination (r2) were also computed.
4.
Results and discussion
As suggested by Ferna´ndez et al. (2001) and Nicolas et al. (2005), sap flow (S in L plant1 d1), in isolated and orchard trees, was linearly related to the PM-FAO-56 grass reference evapotranspiration (E0 in mm d1) and Table 1 summarizes the results. Statistical coefficients were site specific and even for the same species (e.g., apples) the function for one orchard could not be used for the other. It is obvious that under the same E0 conditions the sap flow of irrigated trees will be a positive function of the total canopy leaf area, as implied in the Hatton et al. (1998) sap flow-leaf area relationships. Expressing the
Table 1 – Summary of the statistical relationships (Y = a + bX) between integrated daily sap flow (S, in L plantS1 dS1) and the Penman–Monteith grass reference evapotranspiration (E0, in mm dS1) a
b
r2
RMSE
n
S (L plant1 d1)
0.28 0.02 2.85 1.87 1.01 16.41 36.6
3.09 12.28 4.10 8.85 1.30 13.33 24.42
0.8458 0.8762 0.8555 0.9740 0.5820 0.8492 0.6241
1.39 4.87 2.75 1.63 4.87 6.16 –
23 10 31 8 30 26 59
1.3–13.6 13.4–56.1 6.7–32.9 14.8–39.6 0.8–56.1 28.9–78.6 40–100
Crop Apples dwarf Apples normal Olives Walnut Grapevines Kiwifruit Apricota a
Source: Nicolas et al. (2005).
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Table 2 – Summary of the statistical relationships (Y = a + bX) between integrated daily sap flow per unit leaf area (SA, in L mS2 leafS1 dS1) and the Penman–Monteith grass reference evapotranspiration (E0, in mm dS1) Crop Apples dwarf Apples normal Olives Walnut Grapevines Kiwifruit
a
b
r2
RMSE
n
AL
0 0 0 0 0.47 0.35
0.346 0.346 0.348 0.356 0.195 0.420
0.8450 0.8762 0.8348 0.9698 0.5109 0.8628
0.157 0.129 0.214 0.062 0.182 0.183
23 10 31 8 30 26
8.65 35.5 13.5 26.4 2.76–5.83 32–36.7
AL is the canopy leaf area (in m2).
sap flow per unit leaf area (SA, in L m2 leaf d1) eliminates the effect of canopy size, and the statistical analysis resulted in very similar relationships for most of the orchards (Table 2). For apples (dwarf and normal sizes), olives and walnut trees the y-intercept did not differ statistically from zero and the regression lines were forced through the origin. Pooling the corresponding data seta resulted in the overall regression line SA = 0.348E0 (r2 = 0.8851, n = 72, RMSE = 0.172 L m2 leaf d1). Grapevines and kiwifruit data did not follow this regression, but forcing the regressions also through the origin (for the sake of comparisons) resulted in b = 0.355 for the grapevines, and b = 0.522 for the kiwifruit vines. Discarding the kiwifruit data set from the analysis the weighed average for the regression coefficient was b = 0.349. This empirical function indicates that tree sap flow per unit canopy leaf area corresponds, on average, to 35% of E0. It can be a mere coincidence but b = 0.349 is very close to the inverse of the hypothetical leaf area of the reference grass surface, i.e., 2.881 = 0.347. The statistical results indicate that, on a leaf area basis, tree sap flow does not differ from E0/2.88 (=E288). This is an indication that transpiration on a leaf area basis is very similar regardless of the plant canopy size and shape for most of the plants. Normalizing both flows on a unit leaf area basis reduced the range of the variables to a common interval allowing a better graphical view and comparisons of the dispersion points (Fig. 1). The maximum measured SA was about 2.5 L m2 of leaf d1. Pooling the data for the grapevines, the walnut, the two apple trees (normal and dwarf sizes), and the olives tree the statistical relationship did not differ from
the perfect fit line, that is, SA = 1.01E288 (r2 = 0.8301, n = 102, RMSE = 0.19 L m2 of leaf area d1). However, for the kiwifruit vine transpiration there was a large underestimation of 50%, on average (SA = 1.502 E288; r2 = 0.8065, n = 26), and this special case will be discussed below. As the daily sap flow (S) is equal to SA times the canopy leaf area (AL) and the intention is to predict water use on a daily time scale (Fig. 2), the statistical relationships found between the integrated daily sap flow and the estimated transpiration (E288AL) for each orchard condition is summarized in Table 3. For the walnut, apples, olives and grapevines the slope (b) of the regression lines did not differ statistically from the equal values line (1:1). The daily accumulated sap flow for the walnut tree (26.4 m2 leaf canopy) varied from 14.8 to 39.6 L tree1 d1, and the comparison with the estimated transpiration gave the following statistical relationship: S = 1.026E288AL (r2 = 0.9698, RMSE = 1.63 L tree1 d1, n = 8). RMSE represented about 6% of the average sap flow. For the sake of comparison, using the same data set, the more complex and data intensive scheme used by Green (1993, his Table 1) with computations every 20 min during the day to predict the walnut daily total sap flow (W, L tree1 d1) resulted in S = 1.107W (r2 = 0.8829; n = 9), that is, an under estimation of 10%. The measured sap flow accumulated during the 8 days amounted to 231.6 L, the estimated transpiration added up to 224.5 L with the present scheme, and it summed up to 209.4 L with the Green (1993) short time computations. Surprisingly, the much less intensive approach here proposed gave a better estimate of the daily sap flow.
Fig. 1 – Modified Penman–Monteith FAO-56 evapotranspiration (E288) vs. measured sap flow per unit leaf area of irrigated orchard plants. Inside the parenthesis is the number of days for each case.
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Fig. 2 – Measured vs. estimated total daily sap flow for irrigated orchard apples and olivestrees, grapevines and an isolated walnut tree.
For the apple trees the daily total sap flow and the estimated transpiration had the following statistical fit: S = 0.997E288AL (r2 = 0.9456, RMSE = 2.69 L tree1 d1, n = 33). Sap flow varied from 1.3 to 13.6 L tree1 d1 for the dwarf tree (8.65 m2 of leaf area), and from 13.4 to 56.1 L tree1 d1 for the large tree (35.5 m2 of canopy leaf area). RMSE was about 15% of the average sap flow. During 33 days the sap flow accumulated to 604.7 L and the corresponding estimated transpiration was 607.6 L. Estimated tree transpiration (G, L tree1 d1) given by the more complex computational scheme with the same data set and presented by Green and McNaughton (1997) and Green et al. (2003b) resulted in under estimation of about 9%, or S = 1.09G (r2 = 0.9908, n = 33), and it amounted to 539.8 L (12% difference). Olive tree with 13.5 m2 of leaf canopy had a daily sap flow between 6.7 and 32.9 L tree1 d1. Sap flow versus estimated transpiration did not differ statistically from the perfect fit line, that is, S = 1.003E288AL (r2 = 0.8349, RMSE = 2.54 L tree1 d1, n = 31). RMSE was close to 13% of the average sap flow. Sap flow accumulated to 621.7 L and the corresponding estimated transpiration was 609.2 L. Again, the daily integrated transpiration (O, L tree1 d1) given by the more intensive computational scheme of Green et al. (2002) resulted in S = 1.098O (r2 = 0.8560, n = 31), and the estimated water use during the experiment was 551.3 L (11% difference). Comparisons of the daily accumulated sap flow for the grapevines orchard resulted in S = 0.969E288AL (r2 = 0.5109,
Table 3 – Summary of the statistical relationships (Y = bX) between integrated daily sap flow (S, in L plantS1 dS1) and the estimated transpiration (E288AL, in L plantS1 dS1) Crop Apple trees Grapevines Olives Walnut All crops
b
r2
0.997 0.969 1.003 1.026 1.002
0.9456 0.5109 0.8349 0.9698 0.9679
RMSE 2.69 0.94 2.54 1.63 2.00
S average 18.32 4.51 20.06 28.95 15.62
n 33 30 31 8 102
RMSE = 0.94 L vine1 d1, n = 30) with a much smaller S range (0.8–7.2 L vine1 d1) than for the apples, walnut and olive trees. RMSE represented 20% of the average sap flow. During the experiment the leaf area per vine varied from 5.49 m2 at the beginning to 5.83 m2 a week later, and thereafter it decreased to 2.76 m2 after 35 days. Between two measurements the leaf area was linearly interpolated for the daily calculations. Accumulated sap flow during the experiment was 135.3 L, and the estimated water use added up to 131.5 L. No short-term computations are available for comparison. In regard to the kiwifruit, the 24 h integrated sap flow varied from 28.9 to 78.6 L vine1 d1. Vine leaf area increased from 32 m2, at the beginning of the experiment, to 36.9 m2 after 25 days. The large sap flow underestimation shown in Fig. 1 was caused by the large nighttime transpiration (sunset to sunrise) due to incomplete stomata closure (Judd et al., 1986). Nighttime transpiration is here defined as that occurring during the period of negative net radiation. Water use during the night varied from 2.8 to 21.7 L vine1 d1 and it represented about 26% of the daytime transpiration (ranged from 8 to 57%). Such large values are very similar to those reported by Judd et al. (1986) and Green et al. (1989), also in New Zealand orchards. As before, nighttime sap flow (SN, in L vine1 night1) was positively associated with the nighttime atmospheric vapor pressure deficit (DN, in kPa) and such linear regression relationship (SN = 44.488DN, r2 = 0.9097, n = 25) is displayed in Fig. 3. This regression line also accommodates the results described by Green et al. (1989) and not included in the regression. In a humid coastal climate, with rapid onset of dewfall after sunset, nighttime water use was not detected in a windbreak sheltered kiwifruit orchard (McAneney et al., 1992). There are two possible ways to adjust the predicted sap flow for the kiwifruit vines through the approach here proposed. Analysis of the results shown in Fig. 1 indicate an average difference of 0.5 L m2 of leaf d1 between SA and E288, that is, SA (E288 + 0.5). Fig. 4 shows that indeed the daily integrated sap flow was better estimated this way as the points dispersed around the perfect fit line (S = 1.002[E288 + 0.5]AL, r2 = 0.8474; RMSE = 6.07 L vine1 d1, n = 26).
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159
Fig. 3 – Nighttime sap flow in a kiwifruit vine as a function of the atmospheric vapor deficit during the same period. Results from Green et al. (1989) is shown but not included in the regression.
Fig. 4 – Comparison between the modified Penman– Monteith FAO-56 daily evapotranspiration and the measured sap flow in a kiwifruit vine.
The alternative approach is to add the nighttime sap flow relationship with the vapor pressure deficit, as described in Fig. 3, to the original proposal. In other words, the alternative model is [E288AL + 45DN]. Such approach reduced the under prediction to 9%, on average, or S = 1.09[E288AL + 45DN], r2 = 0.7975; n = 26). In order to have an even dispersion around the 1:1 line, it was found that the second term should go to 60DN. This alternative approach should be preferred as the additional term (SN) vanishes under conditions of nighttime atmospheric vapor pressure saturation (DN = 0). For the sake of comparison, for the same data set, the more complex and more detailed short time scheme with computations for every 30 min throughout the day to predict the 24 h kiwifruit sap flow (K, L vine1 d1) resulted in the following statistical relationship, S = 1.234K (r2 = 0.7957, n = 26). Even though this more intensive data and computational scheme predicts also nighttime transpiration (Green et al., 1989) the under prediction was still large. It is evident that kiwifruit transpiration needs further modeling efforts.
to establish the connection between the reference evapotranspiration and the individual plant water use. The working hypothesis proved valid for canopies with different sizes and exposure to the environment with sap flow varying from 0.8 to 56.1 L plant1 d1, and canopy leaf area from 2.76 to 35.5 m2. In order to become operational it needs an easy way to estimate remotely the tree leaf area throughout the season and many methods are available (Lang and Xiang, 1986; Villalobos et al., 1995; Wu¨nsche and Lakso, 1998; Broadhead et al., 2003; Jonckheere et al., 2004). The present approach eliminates the need of the traditional crop coefficient scheme. As an exception case, it was found that the proposed approach grossly under estimates the kiwifruit sap flow as the leaves continue to transpire at a high rate under nighttime advective conditions. Grass reference evapotranspiration was not able to mimic kiwifruit sap flow under conditions of large nighttime vapor pressure deficits and large nighttime water use. Further adaptation is needed to account for such unusual feature.
5.
Acknowledgement
Conclusions
Results from 102 days of five independent experiments with apples (dwarf and normal sizes), olives and walnut trees and grapevines of different canopy sizes and shapes indicate that, on a daily time scale, the well irrigated canopy transpiration can reliably be estimated through the use of the conventional grass reference evapotranspiration parameterized by the FAO56 bulletin (Allen et al., 1998), with input variables measured at nearby weather stations. Computed reference evapotranspiration is then corrected only by the ratio between the canopy leaf area and the 2.88 m2 of leaf area assumed for the hypothetical reference grass surface. No other empirical correction or adjustment factor was necessary. A remarkably good relationship was found between the estimates and the sap flow determined by compensation heatpulse technique. Integrated daily sap flow was a very good way
This work was partially supported by the Brazilian National Research Council (CNPq).
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