Agricultural and Forest Meteorology 149 (2009) 1063–1072
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Quantifying the uncertainties of transpiration calculations with the Penman– Monteith equation under different climate and optimum water supply conditions Matthias Langensiepen a,*, Marcel Fuchs b, Homero Bergamaschi c, Samuel Moreshet b, Yehezkel Cohen b, Peter Wolff d, Samuel C. Jutzi e, Shabtai Cohen b, Luis Mauro G. Rosa c, Yan Li f, Thomas Fricke g a
Modelling Plant Systems, Institute of Crop Science, Faculty of Agriculture and Horticulture, Humboldt-University of Berlin, Invalidenstrasse 42, 10115 Berlin, Germany Department of Environmental Physics and Irrigation, Institute of Soil, Water and Environmental Sciences Agricultural Research Organization, The Volcani Centre, P.O. Box 6, Bet Dagan 50250, Israel c Department of Forage Plants and Agricultural Meteorology, Federal University of Rio Grande do Sul, Faculty of Agronomy, Caixa Postal 776, CEP 91501-970, Porto Alegre - RS, Brazil d Heiligensta¨dter Weg 5, 37213 Witzenhausen, Germany e FAO Headquarters, Animal Production and Health Division, Viale delle Terme di Caracalla, Rome 00100, Italy f Xinjiang Institute of Ecology and Geography, CAS, 40-3 South Beijing Road, Urumqi, Xinjiang 830011, PR China g Department of Grassland Science and Renewable Plant Resources, Faculty of Organic Agricultural Sciences, University of Kassel, Steinstrasse 19, 37213 Witzenhausen, Germany b
A R T I C L E I N F O
A B S T R A C T
Article history: Received 26 June 2008 Received in revised form 22 December 2008 Accepted 6 January 2009
The uncertainties of transpiration calculations with the Penman–Monteith equation were quantified under different climate conditions of Brazil, Germany and Israel using maize as a common crop type. All experiments were carried out under non-limiting growing conditions. Canopy resistance was determined by scaling to canopy level specific relations between in situ measurements of incident radiation and stomatal conductance using a light penetration model. The model was tested against heatpulse measured sap flow in plant stems. The root mean square error (RMSE) of daily calculated transpiration minus measured sap flow was 0.4 mm/day. It was dominated by its variance component (variance = 0.2 {mm/day}2; bias = 0.0 mm/day). Calculated transpiration closely matched the measured trends at the three locations. No significant differences were found between seasons and locations. Uncertainties of canopy conductance parameterizations led to errors of up to 2.1 mm/day. The model responded most sensitively to a 30% change of net radiation (absolute bias error = 1.6 mm/day), followed by corresponding alterations of canopy resistances (0.8 mm/day), vapour pressure deficits (0.5 mm/day) and aerodynamic resistances (0.34 mm/day). Measured and calculated 30-min or hourly averaged transpiration rates are highly correlated (r2 = 0.95; n = 10634), and the slope of the regression line is close to unity. The overall RMSE of calculated transpiration minus measured sap flow was 0.08 mm/h and was dominated by its variance component (0.005 {mm/h}2). Measured sap flow consistently lagged behind calculated transpiration, because plant hydraulic capacitance delays the change of leaf water potential that drives water uptake. Calculated transpiration significantly overestimated sap flow during morning hours (mean = 0.068 mm/h, n = 321) and underestimated it during afternoon hours (mean = 0.065 mm/h; n = 316). The Penman–Monteith approach as implemented in the present study is sufficiently sensitive to detect small differences between transpiration and water uptake and provides a robust tool to manage plant water supply under unstressed conditions. ß 2009 Elsevier B.V. All rights reserved.
Keywords: Transpiration Penman–Monteith Uncertainty analysis Climates Plant–water relations
1. Introduction Crop transpiration is the main process depleting water from the soil. It affects the sustainability of water resource and conditions the rate of plant growth. The Penman–Monteith equation is widely used to evaluate crop canopies transpiration rates (Burman, 2003; Allen et al., 1998). It combines supply of energy and transport of
* Corresponding author. E-mail address:
[email protected] (M. Langensiepen). 0168-1923/$ – see front matter ß 2009 Elsevier B.V. All rights reserved. doi:10.1016/j.agrformet.2009.01.001
water vapour from the canopy. The effect of plant physiology is taken into account by introducing a stomatal conductance. To resolve the energy balance equation the slope of the saturation vapour-pressure function in the vicinity of air temperature is used to eliminate surface temperature. The steady state assumption implied in the model has been criticized, but the associated calculation error is insignificant because the volumetric heat capacity of plant leaves is very small (Monteith and Unsworth, 1990; McArthur, 1990; Milly, 1991). Net radiation, air humidity, air temperature and wind speed are the required input variables of the equation. Soil heat flux is also
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Nomenclature Ah c d e g E G L P0 r R
s T u0 z Z
g ea rcp x L
solar radiation absorptivity cloudless portion of the sky displacement height in m vapour pressure in Pa (subscripts s = saturation, a = actual) stomatal conductance in m s1 (subscripts s = sunlit, sh = shaded, x = leaf fraction) transpiration in W m2 (subscripts p = potential, a = actual, x = leaf fraction) orthogonal projection of a unit leaf area in the direction of an incident ray latent heat of vaporization in J g1 probability for a incident ray to meet a gap in the foliage resistance in s m1 (subscripts u = aerodynamic, c = canopy, b = leaf boundary layer, x = leaf fraction) radiation flux density in J m2 s1 (subscripts n = net, S = solar, L = longwave (terrestrial), dir = direct, diff = diffuse, x = leaf fractions, s = sunlit, sh = shaded, PAR = Photosynthetically Active Radiation in mmol m2 s1) slope of the saturation vapour pressure curve in Pa K1 temperature in K (subscripts a = air, x = leaf fraction, s = sunlit, sh = shaded) wind speed at the canopy top in m s1 height or roughness length in meter (subscripts o = momentum, E = vapour) solar zenith angle in radian psychrometric constant in Pa K1 emissivity of the atmosphere at air temperature in K volumetric heat capacity of the air in J m3 K1 hemispherical integral of ray interception probability leaf area index in m2 m2 (subscripts s = sunlit, sh = shaded)
required as input, but decreases exponentially from 50 to 5% of net radiation as the surface advances from bare to full vegetation (Choudhury et al., 1987; Baldocchi et al., 1991; Sauer and Horton, 2005). It can thus be neglected when a plant canopy is fully closed. The equation has been parameterized with various degrees of complexity, for time scales ranging from minutes to days, and tested by a variety of methods, including micrometeorological, lysimetric, soil moisture-based and sap-flow measurements of transpiration. Efforts to standardise its application to manage irrigation have lead to formulations compromising between scientific accuracy and practical convenience (Allen et al., 1998). Transpiring plant leaves are usually dry even when water availability in the root zone is unlimited. The surface resistance to water vapour flow of the dry layer separating the atmosphere from the liquid water in the plant tissues has a crucial influence on the magnitude of transpiration. Determining and modelling this resistance remains a partially resolved issue (Brutsaert, 2005). A large number of validation studies have been carried out with lysimeters, which have known technical limitations and confound plant transpiration and soil evaporation (Allen and Howell, 1991). The purpose of this study was thus to quantify the uncertainties of transpiration computations with the Penman–Monteith equation
under contrasting climate conditions using identical parameterization and validation methodologies. The model computations were compared against sap flow measurements that extent and integrate over a period of between 5 and 10 min (Cohen et al., 1988; Cohen and Li, 1996). Aiming for a practical application of the model, a simple approach to determine the surface resistance was chosen for closed canopy conditions when the soil is a negligible source of heat and vapour. It is based on an empirical determination of stomatal light response and scaling to the canopy level using a frequently used procedure to estimate incident canopy radiation in uniform canopies (Fuchs et al., 1987; Sinoquet et al., 1993). Sensitivity, parameter uncertainty and validation analyses were carried out under the contrasting climate conditions of Brazil, Germany and Israel using maize as a common experimental crop type. Previous sensitivity analyses have focussed on the scientific aspects of aerodynamic and canopy resistance parameterizations (Beven, 1979; Saxton, 1975; Verhoef and Allen, 1998; Rana and Katerji, 1998). The complexity of the required experimental setup confined these studies to particular geographical locations. Theoretical studies have dealt with quantifications of stomatal responses to the environment (Eamus and Shanahan, 2002), their scaling to the canopy level (Baldocchi et al., 1991) and comparison of different competitive model theories (Coleman, 1976). The purpose of this study was to provide experimental evidence for the universal validity of the Penman–Monteith theory under contrasting climate and non-limiting water supply conditions. 2. Model Transpiration rates from the sunlit and shaded leaf fractions are calculated separately to account for their different contributions to total transpiration (Fuchs et al., 1987; Petersen et al., 1992). Potential transpiration was estimated with (Penman, 1948): E p;x ¼
1 sþg
½es ðT a Þ ea s Rn;x þ rc p r u;x
(1)
where Ep,x is the transpiration from each leaf fraction x (subscripts p = potential, s = sunlit leaf fraction, sh = shaded leaf fraction) in W m2, s the slope of the saturation vapour pressure curve in Pa K1, g the psychrometric constant in Pa K1, Rn the net radiation flux density at the sunlit or shaded canopy surfaces x in J m2 s1, rcp the volumetric heat capacity of the air in J m3 K1, es(Ta) and ea the saturation and actual vapour pressures in the air at temperature Ta in Pa, and ru,x is the aerodynamic resistance in s m1. The actual transpiration from each leaf fraction Ea,x in W m2 (subscript a = actual) was then calculated with (Monteith, 1965): Ea;x ¼
E p;x 1 þ ðg =ðs þ g ÞÞðr c;x =r u;x Þ
(2)
where rc,x is the canopy resistances of the sunlit or shaded leaf fractions in s m1. Ep,x and Ea,x were converted to mass flux rates by dividing their values by the air temperature dependent latent heat of vaporization of water in J kg1(Cambpell and Norman, 1998). Direct radiation penetrates the canopy through gaps in the foliage. The probability P0 that a ray meets a gap is calculated with the Beer–Lambert law (Sinoquet et al., 1993): P 0 ¼ exp GL=cos Z
(3)
where L is the measured leaf area index and Z the solar zenith angle which is determined with a Fourier series (Spencer, 1971). Assuming a spherical leaf angle distribution G, the orthogonal projection of a unit leaf area in the direction of an incident ray equals 0.5. The probability of diffuse incident radiation penetration
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into the canopy was computed by numerically integrating the directional gap probabilities over 18 zenith angle classes. The sunlit leaf area index Ls was determined by dividing the fraction of intercepted light by the shadow by a unit leaf area on a horizontal plane:
Ls ¼
1 P0 G=cos Z
(4)
The shaded leaf area index Lsh is then L minus Ls. Agricultural crop leaves typically have a solar absorptivity Ah of 0.55 (Gates, 1980; Cambpell and Norman, 1998). Using this value and assuming that they receive direct radiation plus a single scatter, net shortwave radiation per unit sunlit leaf area index RS,n,s in W m2 was calculated with (Fuchs et al., 1987, Bugler, 1977): RS;n;s ¼ A0:5 h
RS;dir 0:5 cos Z þ RS;diff
(5)
where RS,dir and RS,diff are the estimated direct and diffuse components of global radiation (subscripts n = net; dir = direct; diff = diffuse; S = Solar). As shaded leaves exchange radiation more than once, the model assumes that 95% of diffuse solar radiation is eventually absorbed amongst them when the canopy is closed RS;n;sh ¼ 0:95RS;diff
(6)
Significant net terrestrial radiation exchange is assumed to take place only between sunlit leaves and the cloudless portion of the sky c from which shaded leaves are sheltered. The net terrestrial radiation RL,n,s exchange in W m2 of this fraction is (subscript L = longwave, terrestrial): RL;n;s ¼ 5:67 108 cxð1 ea ÞTa4
(7)
where the numeric coefficient is the Boltzmann constant in W m2 K4, ea the emissivity of the atmosphere at air temperature Ta in Kelvin (Brutasert, 1982), and x is the hemispherical interception probability solved by numerically integrating ray interception probability over 18 zenith angle classes. RL,n,s is also used to determine the maximum rate of dew formation, Ep in g m2 (subscript p = potential) during nighttimes when solar radiation and vapour pressure deficits are zero (Garrat and Segal, 1988) Ep ¼
sRL;n;s Lðs þ g Þ
(8)
where L is the latent heat of vaporization. If negative net radiation cools the top canopy layer below dewpoint temperature water condenses there, but in dense canopies heat supply from the soil prevents dew in the lower foliage (Jacobs et al., 1996). Eq. (1) estimates evaporation of the dew until its depletion. The net radiation balances of the sunlit and shaded canopy fractions are Rn;s ¼ RS;n;s RL;n;s Rn;sh ¼ RS;n;sh
(9) (10)
Stomatal responses to photosynthetically active radiation were calculated using an empirical function with two fitting parameters, a and b, determined under non-limiting soil water supply conditions (Petersen et al., 1992): g s;x ¼ a
pffiffiffiffiffiffiffiffiffi RPAR þ b RPAR
(11)
where gs,x is the stomatal conductance in m s1 and RPAR the photosynthetically active radiation in mmol m2 s1 (subscript PAR = photosynthetic active radiation). The model scales leaf
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resistance to the sunlit and shaded canopy levels using r c;X ¼
1 g S;X LX
(11a)
It computes their solar radiation loads and converts them to the photosynthetic active spectrum (Rochette et al., 1991) assuming a constant proportionality factor of 2.04 between measured solar radiation and photosynthetically active radiation (Ross, 1981). The characteristic width of sunlit and shaded maize leaves was set to 0.1 m and their boundary layer resistance rb,x was calculated with (Cambpell and Norman, 1998): sffiffiffiffiffiffiffi 0:1 r b;x ¼ 300 (12) u0 where u0 is the wind speed at the canopy top in m s1 extrapolated by the logarithm profile law, which was also used to calculate the turbulent resistance ra: ra ¼
lnð½z d=z0 Þlnð½z d=zE Þ 2
k u
(13)
where u is the wind speed at height z, k the von Karman constant (0.4), d the displacement height taken as 66% of the corn canopy height h in meter, z0 the moment roughness length (0.13 h) and zE is the roughness length for vapour transport (0.2 z0). The total aerodynamic resistance is finally calculated by coupling the turbulent and boundary layer resistances in series: r u;x ¼ r a þ
r b;x
Lx
:
(14)
3. Materials and methods The studies were carried out during the 1995 and 1996 vegetation seasons under the contrasting climate conditions of Brazil, Germany, and Israel. Corn was chosen as a common experimental crop for this study. The experiment at Brazil was located at Eldorado do Sul (Latitude 30860 S, longitude 518410 W, altitude 40 m above sea level) which has a subtropical climate with hot summers and high rainfall during most of the year except during peak summer. The climate at Hebenshausen in Germany (Latitude 518230 N, longitude 98550 E, altitude 250 m above sea level) is humid temperate with occasional frosts during winter and an even rainfall distribution throughout the rest of the year. The experiment at Israel was carried out in Bet Dagan (328010 N, 348500 E, 25 m above sea level) in a typical semi-arid climate zone with hot and dry summers and warm winters with infrequent rainfall. 3.1. Agronomic details The plot at the Brazilian site had a size of 0.54 ha (62 m 87 m). Its soil is a well-drained humic sandy loam. Maize (cv. Pioneer 3230) was sown with a density of 6.7 plants m2 at the end of October. Row spacing was 0.7 m. The surrounding fields were also cultivated with crops. A line-source sprinkler system was installed to maintain the water content of its adjacent soils at field capacity. The corresponding irrigation amounts were calculated from daily evapotranspiration measurements which were carried out with a weighing lysimeter located in the field center (surface 5.1 m2, depth 0.9 m). The soil at the German site region is classified as a humic loess type with slight stagnic conditions at 1.2 m depth. Maize (cv. Helix, KWS) was sown with a density of 11 plants m2 at the end of April 1995 and 1996 on commercial farm fields of 2.7 ha (150 m 180 m) sizes; row spacing was 0.7 m. The fields were surrounded by
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Fig. 1. Leaf area index (LAI), plant height (h), and computation periods (dotted lines) at the three experimental sites.
agricultural crops. The crops did not experience extended drought periods due to frequent summer rains during both years. The experiment at Israel was carried out on a 0.42 ha (65 m 65 m) plot located in a large field crop research area. Its soil is a sandy loam. Sweet corn (cv. Jubilee) was hand-sown in June at a density of 8 plants/m2; row spacing was 0.95 m. Soil moisture was allowed to drop to 80% of field capacity level and then replenished to full retention using drip irrigation. Fertilizer dosages, pest and disease control were applied according to standard agronomic practice in all experiments. 3.2. Model parameterization and input data collection Leaf vapour conductance and photosynthetically active radiation were measured with steady state porometers (L1600 M, Licor, Lincoln, NE, USA). Conductance readings were taken from the abaxial and adaxial leaf sides. The measurement locations were sampled at random in the sunlit and shaded canopy portions. Frequent dewfall and ensuing canopy surface drying prevented porometer measurements before 10 a.m. in the German trial. Furthermore morning and afternoon readings of stomatal light responses may differ (Li et al., 2004). Only noon observations were chosen for model parameterization to avoid artefacts from stomatal acclimation to steep changes of physical air states and the light environment during mornings and afternoons. Leaf area growth was monitored at all locations by destructive and indirect methods (LI-3100C Area Meter, LI-2000 Fisheye, Licor, Lincoln, NE, USA; SUNLINK, Decagon Devices, Inc., Pullman, WA, USA). Plant heights were measured with rulers. Seasonal data and periods during which computations were carried out are shown in Fig. 1. The model was exclusively applied under closed canopy conditions when leaf area index was above 2.5. Solar radiation, wind-speed, air temperature and humidity were monitored at 2 m height above grass surfaces and averaged over 30-min intervals using standard automatic weather stations operated in close vicinity of the experiments (Campbell Scientific Inc., Logan, UT, USA; Thies Clima, Go¨ttingen, Germany). This is a typical procedure to obtain and use weather data for model applications under practical agronomic conditions which was thus also applied in this study. Since the structural properties of grass and maize canopies could have potentially influenced the
temperature and humidity characteristics of the surface boundary layer, we examined the validity of this approach. Additional meteorological towers were installed above the maize canopies for this purpose. The heights of the sensors were adjusted weekly to 0.66 maize height + 3 m. Differences in data outputs from the meteorological station pairs were small in the cases of the relatively small plots in Brazil and Israel. Strong air mixing with the surrounding atmosphere prevented a build-up of a new boundary layer. Fetch requirements were only met in the cases of the larger fields in Germany and thus allowed for a testing of the chosen approach. Temperature and humidity fluctuations measured with both stations were almost identical in 1995 and 1996. The calculated vapour pressure deficits above the grass and maize surfaces are thus highly correlated (Fig. 2). At low vapour pressure deficit, humidity over the maize canopy is higher than over grass. During nighttime temperature inversion more dew can be stored on the larger surface of the maize canopy above which stable atmosphere promotes vapour accumulation. The overall difference of 2% is small enough to allow for a usage of both station outputs interchangeably.
Fig. 2. Correlation between air vapour pressure deficits measured above grass and maize canopy surfaces during the main growing periods in 1995 and 1996 at the German field sites.
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3.3. Validation, sensitivity and uncertainty analyses The sap flow of eight randomly selected plants with same stem diameters was determined in each field experiment with the calibrated heat pulse method (Cohen et al., 1988). The temperature drift between the upstream and downstream sensors was monitored for 2 min before each measurement and subtracted from the flow dependent temperature change measured over a period of between 5 and 10 min. A constant calibration factor of 1.6 (Cohen and Li, 1996) was used in all corn. Each set of diurnal sap flow measurements was filtered to remove data inconsistencies generally due to improper installation. Group average was used to attenuate noise at extremely low sap flow rates. Mean sap fluxes and their standard deviations were used in the validation, sensitivity and uncertainty analyses. We emphasize that the heat pulse measures sap flow and not transpiration. The comparison of the measurements with the model calculations entails the assumption that plant hydraulic capacitance is small. Model calculation accuracies were measured with several statistical methods (Zar, 1999): Sap flow versus calculated transpiration regression and correlation analyses were carried out to determine the overall agreement between both independent methods. The root mean square error (RMSE) of calculated transpiration minus sap flow was additionally determined and decomposed into bias and variance components to trace the different error sources. Daily calculated transpiration minus sap flow data were also used in a sensitivity analysis to check the interactive influences of altered net radiation and vapour pressure inputs on computation bias errors. Seasonal and characteristic daily trends of calculated transpiration and sap flow provided information about the dynamic changes of both independent methods. The effects of uncertainties of stomatal conductance measurements on model bias and variance errors were finally analysed within the 95% range of predictions bands of the fitted stomatal light response function. All analyses were carried out with the statistical software R (R Development Core Team, 2006). 4. Results The Penman–Monteith equation was tested in the typical weather of the summer growing seasons in Brazil, Germany, and Israel. Measured and calculated transpiration rates were highly correlated (r2 = 0.95; n = 10,634), and the slope of the regression line is close to unity (Fig. 3). Differences between the root mean square errors of calculated transpiration minus sap flow deter-
Fig. 3. Sap flow versus calculated transpiration. The RMSE of calculated minus sap flow transpiration was 0.08 mm/h (Variance = 0.00615 {mm/h}2, Bias = 0.0006 mm/h).
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mined under different climatic and seasonal conditions were insignificant. The overall RMSE of 0.08 mm/h is dominated by its variance component (0.005 {mm/h}2). Data scattering is particularly high at low sap flow rates. Deviations between calculated daily transpiration and sap flow with their variances are shown in Fig. 4. Transpiration fluctuations at the semi-arid location of Bet-Dagan were relatively small compared to the sub-tropical and temperate sites at Eldorado do Sul and Hebenshausen. Calculated transpiration did not systematically depart from measured plant water uptake at any time. Both independent methods agreed very well when transpiration was above 3 mm/day, but increasingly departed from each other below this level. The differences between calculated transpiration and sap flow were highly significant in case of the German experiment carried out during the 1996 season, which was marked by frequent cloud, rain and fog occurrences under moderate temperature conditions which led to frequent drops in transpiration rates. The RMSE, bias and variance of daily calculated transpiration minus sap flow quantify how uncertainties about stomatal conductance impaired the predictive quality of the model. Fig. 5 shows the fitted stomatal light response functions for each season and cultivar together with their confidence and tolerance bands. Although midday leaf conductances are strongly correlated with incident PAR, data scattering is large. The cultivar specific responses differed considerably amongst the sites. Seasonal differences were comparatively small. The fitted light response function was replaced by its upper and lower bounds to calculate their effects on the model (Table 1). Mean transpiration was systematically underestimated by 2.1 mm/day with the lower bound and overestimated by 1.7 mm/day with the upper bound. Variances were practically unaffected by these changes. Net radiation and vapour pressure deficit (VPD) are the principal meteorological variables driving transpiration in the Penman–Monteith equation. Errors in determining leaf area and/or radiative fluxes significantly influence the accuracies of net radiation computations. Malfunctioning humidity and temperature sensors corrupt VPD. A sensitivity analysis altering the netradiation and VPD fractions evaluated their interactive effect on the accuracy of calculated transpiration. Fig. 6 shows the resulting calculation errors in mm/day (z-axis of the contour plot). VPD changes ranging between the 0.7 and +1.3 fractions of the original level produced bias errors between 0.2 and 0.5 mm/day. Corresponding changes of net radiation computations produced considerably larger model bias errors which ranged between 1.22 and 1.6 mm/day. The previous results demonstrate that high computation accuracies can be achieved on a daily basis when the Penman– Monteith equation is properly parameterized. They do not provide confidence, however, about the quality of short-term predictions of this method which produced mixed results in the low transpiration range (Fig. 3). One characteristic diurnal was chosen from each country’s data set to demonstrate the influences of short-term weather perturbations on calculated transpiration and sap flow. The diurnal transpiration course determined under German conditions is shown in Fig. 7A. Evaporation of dew deposited on leaves suppressed transpiration and water uptake between sunrise and 8 a.m. Eq. (1) was used to calculate dew evaporation. A rapid solar radiation rise to 680 W m2 accompanied by air heating and a vapour pressure deficit of 1.7 kPa increased sap flow from zero to 0.8 mm/h between 8 and 12 a.m. Sap flow exceeded calculated transpiration from 11 to 12 a.m. Later thick slow moving clouds caused global radiation and VPD to decrease to 310 W m2 and 1.4 kPa, respectively, lowering the sap flow rate. During the afternoon solar radiation and VPD increased to 520 W m2 and
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Fig. 4. Seasonal courses of sap flow and calculated transpiration under the contrasting climatic conditions of Germany (top), Israel (middle), and Brazil (bottom).
1.9 kPa to which sap flow responded by elevating its rate. In contrast with observations in Brazil and Israel calculated transpiration lagged behind the measured sap flow. Maize transpiration was determined with a higher time resolution of 15 min in the Brazilian experiment allowing a closer analysis of short-term phenomena (Fig. 7B). Low wind speeds and vapour pressure deficits prevented a strong rise in calculated transpiration during the first two morning hours, respectively. Global radiation and VPD rose to 980 W m2 and 3.1 kPa during the subsequent four morning hours. Measured sap flow increased during this period but lagged behind calculated transpiration. Rapid fluctuations of radiation and VPD after 12 a.m. resulted in corresponding fluctuations of calculated transpiration and measured sap flow that dropped from 1.2 to 0.2 mm/h. The weather conditions varied considerably during the subsequent 2 h. Weather conditions normalized afterwards. Global radiation reached a high value of 820 W m2 again and VPD increased to 1.7 kPa. Weather conditions during the remaining daylight hours were characterized by smooth transitions in global radiation and VPD at an average wind speed of 3 m s1. Calculated transpiration consistently lagged behind sap flow transpiration during this time.
The semi-arid climate at Bet-Dagan site provided an opportunity to analyse the discrepancies between calculated transpiration and sap flow courses under continuous hot and dry weather conditions. Any amount of dew would have quickly evaporated shortly after sunrise due to a rapid increase of air vapour pressure deficit. Measured sap flow continuously lagged behind calculated transpiration before and after noon when solar radiation and VPD reached peak values of 980 W m2 and 1.8 kPa, respectively (Fig. 7C). This effect was repeatedly observed with very few exceptions during the two growing seasons. In summary, these results suggest that calculated transpiration consistently overestimates the measured sap flow rate during morning hours and underestimates it during the afternoon. In order to quantify this observation, all validation pairs collected during 9 and 10 a.m. were compared against those obtained between 4 and 5 p.m. (Fig. 8). Sap flow was also set to a lower threshold level of 0.33 mm/h to exclude cloudy days with strong weather fluctuations that would have introduced a considerable degree of noise in this comparison. Sap flow was significantly overestimated in the morning (mean = 0.068 mm/h, n = 321) and underestimated in the afternoon (mean = 0.065 mm/h; n = 316).
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Fig. 5. Stomatal conductance parameterization at Hebenshausen (cv. Helix), Bet-Dagan (cv. Jubilee) and Rio-Grande do Sul (cv. Pioneer 3230).
5. Discussion Calculated transpiration agreed closely with sap flow under the contrasting climate conditions of Brazil, Germany, and Israel, on a daily basis. This observation verifies the general validity of the Penman–Monteith approach, which has been also reported in a number of other studies (Burman, 2003; Brutsaert, 2005). The diurnal courses of measured sap flow lag behind the calculated transpiration (Figs. 7 and 8). Initially in the morning, transpiration driven by meteorological variables depletes water from the plant tissues causing a drop of leaf water potential. In response to this decrease of water potential sap flow increases and therefore lags behind transpiration. In the afternoon, when the atmospheric evaporative demand decreases, a fraction of the sap flow replenishes the water depleted from the plant tissues (O’Brien et al., 2004; Mencuccini, 2003; Ewers and Oren, 2000; Bethenod et al., 2000; Wullschleger et al., 2000; Carlson and Lynn, 1991). The magnitude of the lag is proportional to the hydraulic capacitance of the plant tissues, defined as the change of their volumetric water content per unit change of potential.
The lag between the two diurnal curves is of the order of 30 min suggesting that the hydraulic capacitance of the plants was small. As irrigation and rainfall maintained optimal water supply to the crop during the experiment, transpiration depleted only apoplastic water. In this range the plants remain turgid and their hydraulic capacitance is indeed low (Campbell et al., 1979). However, in water stressed plants that undergo turgor loss symplastic water is removed from the cell vacuoles. Hydraulic capacitance in the symplastic water content range is considerably higher than in the apoplastic range and will increase the phase lag of sap flow. This effect of hydraulic capacitance is shown in Fig. 9 comparing sap flow in stressed and unstressed plants during a sudden thunderstorm. In the unstressed plants the wetting of the leaves by the rain and the low evaporative demand abruptly decreased sap flow rate. A low sap flow, maintained for a short period of time, was sufficient to replenish the small apoplastic capacitor. In the stressed plants the freshly wetted soil and the slowly rising leaf water potential allowed
Table 1 Sensitivity of calculated transpiration to the scatter of stomatal light response data determined by using the season average parameters of the fitted functions shown in Fig. 5 and their lower and upper bounds. Lower bound
Best fit
Upper bound
Brazil RMSE, mm/day Bias, mm/day Variance, {mm/day}2
2.7 2.7 0.2
0.4 0.2 0.1
1.7 1.2 0.3
Germany RMSE, mm/day Bias, mm/day Variance, {mm/day}2
1.9 1.6 0.8
0.6 0.1 0.4
1.5 1.4 0.3
Israel RMSE, mm/day Bias, mm/day Variance, {mm/day}2
2.0 2.0 0.1
0.3 0.1 0.1
2.6 2.6 0.2
Fig. 6. Errors of transpiration computations in mm/day (z-axis) resulting from changes in net radiation (x-axis) and vapour pressure deficit (y-axis) fractions.
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Fig. 7. Typical daily courses of calculated transpiration (closed symbols) and measured sap flow (open symbols): (A) Hebenshausen, Germany (10.8.1996), (B) Eldorado do Sul, Brazil (31.12.1996) and (C) Bet-Dagan, Israel (9.8.1996). Values of relevant global radiation and vapour pressure deficit data are given.
the prolonged sap flow rate needed to recharge the large symplastic capacitor despite transpiration suppression by evaporation from the wetted leaves and the drop of evaporative demand. Evaporation of dew retained on the leaf surfaces could explain that the Penman–Monteith equation overestimates water uptake during early morning hours, particularly under the calm and humid weather conditions of Germany (Herbst et al., 1996). If this had been the case calculated transpiration would have matched the diurnal course of plant–water uptake no later than about 2 h after sunrise, because the maximum amount of dew evaporation in maize canopies is typically below 0.2 mm (Jacobs et al., 1996; Fuchs et al., 1989). This behaviour was not detected during the entire experiment. Therefore, dew retention is not responsible for the phase shift between the sap flow and calculated transpiration. The Penman–Monteith equation is most significantly applied in water balance studies where short-term phenomena play a comparatively minor role. However, it matches also closely the diurnal course of plant water uptake. It precedes systematically sap flow measurements. The phase shift amounts to around 30 min, which are also the time step of the calculations and the measurements. Hydraulic capacitance of the plants accounts easily for the small discrepancy. The most important goal of this study was to quantify the effects of uncertainties of canopy resistance, faulty net-radiation and vapour pressure deficit on daily transpiration. Canopy
resistance was determined with a simple methodology using an empirical stomatal light response curve that was scaled up to the whole canopy by means of a light interception model. This approach facilitates a simple application of the Penman– Monteith under practical conditions (Baldocchi et al., 1991), such as irrigation scheduling or regional hydrological studies. The maximum computation error introduced by the statistical uncertainties of stomatal resistance parameterizations (Fig. 5) was 2.7 mm/day under the conditions of this study, which is quite significant (Table 1). Altering the relation between PAR and stomatal conductance measurements by leaf twisting, insufficient chamber acclimation and drying of desiccants are usually the major sources of this uncertainty (Turner, 1991). Physiological reasons could also be made responsible for these uncertainties. Li et al. (2004) detected different stomatal light responses in maize during mornings and afternoons, slight under unstressed and more severe under stressed conditions, suggesting environmental control of stomatal opening that was not considered in this model. Diurnal changes of temperature, humidity and soil matric potential may cause additional variations of stomatal conductance. Based on a comprehensive computation exercise, Tuzet et al. (2003) came to the conclusion that stomatal conductance cannot be modelled using leaf-level processes alone, but the effect of environmental factors is small when soil water supply is optimal. For this reason the simple scaling methodology based on sole canopy architectonic and light information applied in the present study remains valid and
Fig. 8. Morning–afternoon segregation of the comparison between calculated transpiration and measured sap flow rate.
Fig. 9. Measured sap-flow rates under optimum and severe water stress on a day with a sudden thunderstorm (Rio Grande do Sul, Brazil, 13.1.1997). Vapour pressure deficit (VPD) and global radiation (Rglob) conditions are shown for the noon (12 a.m.–3 p.m.) and after-thunderstorm periods (4–9 p.m.).
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is corroborated by the experiments. The study also shows that the shape of the stomatal light response is cultivar dependent and cannot be generalized. Canopy architecture and measured solar irradiance also determine the magnitude of the net-radiation term of the Penman–Monteith equation. Changing its value by 30% led to maximum computation errors of 1.6 mm/day in this study, which were high compared to corresponding changes in vapour pressure deficit which produced errors of up to 0.5 mm/day (Fig. 6). These observations confirm results of other studies demonstrating the effects of both variables on the Penman– Monteith calculations (Yoder et al., 2005). Leaf area development and meteorological data must thus be accurately determined to ensure good results. 6. Conclusion The results of this study confirm that the Penman–Monteith equation is a robust tool for daily and diurnal computations of plant transpiration under different climate conditions. Its reliability is primarily influenced by canopy resistance parameterization and accuracy of input variables which determine the magnitude of net-radiation. The diurnal course of measured sap-flow consistently lagged behind calculated transpiration, due to plant hydraulic capacitance. Acknowledgements We thank family Wentrot at Hebenshausen for their friendly support and providing access to their maize fields at no costs. Tobias Gabele and Tobias Wilhelm assisted during field work. Rainer Braukmann, Dr. Dorothea von Renesse and Marina Hethke-Wesche from the Department of Tropical and Subtropical Field Crop Production at the University of Kassel provided technical support. Renate Curdt and Hans Heman administered the project. The field experiments in Bet Dagan were conducted with the technical help of Yefet Cohen. We also thank UFRGS (Universidade Federal do Rio Grande do Sul), CNPq (Conselho Nacional de Desenvolvimento Cientı´fico e Tecnolo´gico) and Fundac¸a˜o CAPES for sponsoring great part of the Brazilian staff and materials for the cooperative research activities. This study was financed by the German Ministry of Economic Cooperation through the German-Israel Agricultural Research Agreement for the Benefit of Third-World Countries (GIARA). We gratefully acknowledge the support from Dr. S. Gura and Mr. R. Korntheuer. References Allen, R.G., Howell, T.A., 1991. Lysimeters for evapotranspiration and environmental measurements. In: Proceedings of the International Symposium on Lysimetry. American Society of Civil Engineers, Reston. Allen, R.G., Pereira, L.S., Smith, M., 1998. Crop evapotranspiration: guidelines for computing crop water requirements. FAO Irrigation and Drainage Papers 56: Food and Agriculture Organisation of the United Nations, Viale delle Terme di Caracalla, Rome 00100, Italy. Baldocchi, D.A., Luxmoore, R.J., Hatfield, J.L., 1991. Discerning the forest from the trees: an essay on scaling canopy conductance. Agric. For. Meteorol. 54, 197– 226. Bethenod, O., Katerji, N., Goujet, R., Bertolini, J.M., Rana, G., 2000. Determination and validation of corn transpiration by sap flow measurement under field conditions. Theor. Appl. Climatol. 67, 153–160. Beven, K., 1979. A sensitivity analysis of the Penman–Monteith actual evapotranspiration estimates. J. Hydrol. 44, 169–190. Brutasert, W.R., 1982. Evaporation into the Atmosphere. Kluwer, Dordrecht, Netherlands. Brutsaert, W., 2005. Hydrology. Cambridge University Press, United Kingdom.
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