SINGLE-LAYER EVAPOTRANSPIRATION MODEL WITH VARIABLE

SINGLE-LAYER EVAPOTRANSPIRATION MODEL WITH VARIABLE CANOPY RESISTANCE By Mladen Todorovic1 ABSTRACT: A new approach to modeling canopy resistance is presented as an alternative to the Food and Agricultural Organization of the United Nations Penman-Monteith method with the constant canopy resistance. The evapotranspiration (ET) model is based on the ‘‘big-leaf’’ approach and a variable canopy resistance. The model’s input requires standard meteorological data as in the Penman-Monteith combination approach. The model was validated using weather and grass lysimeter data measured on an hourly basis at Davis, Calif., and on a daily basis at Policoro, Southern Italy. ET estimates from the model were compared with the results of ET values obtained by the Food and Agricultural Organization of the United Nations Penman-Monteith approach using the constant canopy resistance rc = 70 s m⫺1. The results showed a very convincing performance of the model for estimating reference ET on both an hourly and daily basis. This work confirms that the canopy resistance depends on climate, and that a variable rc is recommended for ET models. The proposed model does not introduce any empirical parameter, does not require calibration for the two sites tested or for different time scales, and it is simple enough for direct practical application.

INTRODUCTION The Penman-Monteith combination equation is widely accepted as the best performing method for evapotranspiration (ET) estimates from the surfaces with either optimal or limited water supply (Smith et al. 1991; Allen et al. 1994a.b, 1998). However, the application of the Penman-Monteith approach is limited by the lack of knowledge about the canopy resistance term. There are many examples of work done to link the Monteith’s resistance term to easily obtainable climatic variables (Bailey and Davies 1981; Jarvis 1981; Allen 1986; Stewart and Gay 1989; Kim and Verma 1991; Stewart and Verma 1992). To estimate ET, some workers have dealt either with the ratio of actual to maximum ET rate (McNaughton and Jarvis 1983, 1984; Jackson 1985) or with the ratio between ‘‘equilibrium’’ (vapor pressure deficit approaches to zero) and potential ET (Priestley and Taylor 1972). Bouchet (1963) used the potential and actual ET as complementary values. Allen et al. (1989) proposed the use of a constant daily value for canopy resistance rc = 70 s m⫺1 in the estimate of reference grass ET. This simplification of the canopy resistance term provided very good results in numerous comparative studies (Allen et al. 1989, 1994b; Jensen et al. 1990; Allen and Fisher 1990, 1991; Choisnel et al. 1992) and demonstrated its usefulness in the application of the Penman-Monteith equation for estimating reference ET. In 1990, the expert group of the Food and Agricultural Organization of the United Nations (FAO) on ‘‘Procedures for revision of FAO guidelines for prediction of crop water requirements’’ unanimously recommended the Penman-Monteith combination equation as the best performing method for the estimation of reference ET (Smith et al. 1991). Notwithstanding that the canopy resistance depends on weather variables and vegetation physiological status, Smith et al. (1991), at the current state of the art, suggested for practical purposes the use of the Penman-Monteith equation with constant canopy resistance (rc = 70 s m⫺1) in reference grass ET. They also

proposed the new definition of reference ET with a standardized hypothetical crop having the constant height and value of canopy resistance. However, Smith et al. (1991) recommended further studies to improve the new reference ET concept and to develop methods for modeling canopy resistance. In this regard, the approach for reference ET estimate herein is based on the Penman-Monteith combination concept and the variable canopy resistance modeled by means of weather parameters that are measured at the reference height above the canopy as in the FAO Penman-Monteith approach. MODEL DESCRIPTION The model presented here deals with the difference between potential and actual latent heat flux, assuming that it is caused by an additional sensible heat flux imposed to heat the evaporating surface—the canopy—to provide the extra energy to move saturated air out of vegetation elements (Todorovic 1997). The two particular states (potential and actual) of the plant-atmosphere interaction are compared to approach an ET from the canopy. The potential state refers to potential ␭ETp , i.e., to evaporation of liquid water from the surfaces that are externally wet. This process is controlled by meteorological factors only and may be expressed by the Penman’s form of the combination equation: ␭ETp =

⌬A ⫹ ␳CpD/ra ⌬⫹␥

(1)

where A = (Rn ⫺ G) represents the available energy for ET, the net radiation flux density Rn minus the soil heat flux density G; D = vapor pressure deficit of air; ␳ = mean air density; Cp = specific heat of moist air; ⌬ = slope of the curve relating saturation vapor pressure to temperature; ␥ = psychrometric constant; and ra = aerodynamic resistance—a function of wind speed and roughness characteristics of the vegetation. In this case, the energy balance equation may be written as A = ␭ETp ⫹ H

(2)

1

Res. Sci., Int. Ctr. for Advanced Mediterranean Agronomic Studies— the Mediterranean Agronomic Inst. of Bari, Via Ceglie 9, 70010 Valenzano (BA), Italy. Note. Discussion open until March 1, 2000. To extend the closing date one month, a written request must be filed with the ASCE Manager of Journals. The manuscript for this paper was submitted for review and possible publication on May 27, 1998. This paper is part of the Journal of Irrigation and Drainage Engineering, Vol. 125, No. 5, September/ October, 1999. 䉷ASCE, ISSN 0733-9437/99/0005-0235–0245/$8.00 ⫹ $.50 per page. Paper No. 18418.

where the sensible heat flux H in (2) has a positive sign if it is oriented upward (i.e., away from the evaporating surface), and it has a negative sign if the sensible heat flux is directed downward (i.e., toward the evaporating surface). On the other hand, the actual state refers to ␭ET from a vegetated evaporating surface that is not externally wet. This significantly changes the concept because ET originates within the vegetation elements (stomatal cavities) and the resistance

JOURNAL OF IRRIGATION AND DRAINAGE ENGINEERING / SEPTEMBER/OCTOBER 1999 / 235

of the evaporating surface should be taken into account. Assuming certain resistivity of the plant canopy to the water vapor exchange between the canopy and surrounding air, Monteith (1965, 1973) introduced the canopy resistance term rc , and the equation [(1)] for the potential ET rate changes to the form of the well-known Penman-Monteith equation for the estimation of actual evapotranspiration rate ␭ET =

⌬A ⫹ ␳cp D/ra ⌬ ⫹ ␥(1 ⫹ rc /ra)

(3)

where if rc > 0 then ␭ET < ␭ETp . The water vapor flux, to overcome the additional resistance rc , needs more energy with respect to the free water surface, and consequently, this changes the energy status of the atmosphere. A decrease of latent heat flux into the atmosphere is balanced by an increase in the amount of sensible heat drawn from the available energy. Because the total energy content in both states (potential and actual) remains constant and the presence of the plant community introduces a certain resistivity to the water vapor flux rc > 0, the actual latent heat flux ␭ET is lower than its potential counterpart ␭ETp , and the energy balance equation may be written as A = ␭ET ⫹ H ⬘ ⫹ H

(4)

H ⬘ = ␭ETp ⫺ ␭ET

(5)

where

represents the difference in the fluxes between potential and actual ET. This additional sensible heat flux H ⬘ is directed upward and it is generated through the temperature difference between evaporating surface with rc = 0 and rc > 0. This concept is illustrated in Fig. 1, assuming the analogy between the single leaf and the ‘‘big leaf ’’ representing a canopy. Again, two particular states of the vegetation-atmosphere system are examined. If the vegetated surface is fully wet, then rc = 0, ␭ET = ␭ETp , and the air is assumed to be saturated at the level d ⫹ z0, which is the mean level of sources-sinks for sensible heat and water vapor. When rc = 0, the sensible heat flux H accounts only for the temperature difference between Ts and T, where Ts is the canopy temperature and T is the air

temperature at the reference height. The sensible heat flux H is oriented upward when Ts > T, it is oriented downward when Ts < T, and it is zero when Ts = T. The sensible heat flux does not account for the H ⬘, which is equal to zero because no additional energy is needed to extract the water out of vegetation elements. However, if the vegetated surface is not saturated at level d ⫹ z0 then rc > 0, ␭ET is less than ␭ETp , and part of the energy supply to the canopy that would have evaporated water heats the vegetation instead. This raises the canopy temperature by an amount t = T ⬘ ⫺ Ts . The additional sensible heat flux H ⬘ is a small difference in sensible heat flux due to the fact that a canopy with rc > 0 will have a temperature T ⬘ = Ts ⫹ t rather than Ts . Because the temperature is higher, this component of total sensible heat flux will be in the upward direction. Therefore, the total sensible heat flux density H *, driven by the flux gradient between the saturated level and the reference level, may be expressed as H* = H ⫹ H⬘ =

␳cp(Ts ⫺ T ) ␳cp t ⫹ raH r⬘

(6)

where H⬘ =

␳cp t r⬘

(7)

is a part of the sensible heat flux density accounting for the difference between ␭ETp where rc = 0 and ␭ET where rc > 0. In (7), r ⬘ presents the ‘‘pseudo’’ resistance term to the additional heat transfer between the evaporating plant surfaces and d ⫹ z 0. Then, combining (1), (3), and (7) into (5), and rearranging the terms, one obtains A

冉

⌬⫹␥

冊

ri ra

␥ ⌬⫹␥

rc ␳cp t = rc ra r⬘ ⌬⫹␥⫹␥ ra 1

(8)

where ri =

␳cp D ␥A

(9)

is the so-called climatological resistance widely used in the

FIG. 1. Analogy between Single Leaf (Stomata) and Big Leaf (Canopy) Saturation Level for Actual State of Vegetation-Atmosphere System 236 / JOURNAL OF IRRIGATION AND DRAINAGE ENGINEERING / SEPTEMBER/OCTOBER 1999

literature (Monteith 1965; Stewart and Thom 1973; Thom 1975; Jarvis 1981; Monteith and Unsworth 1990). Because the pathway of water vapor and sensible heat between the evaporating plant surface and level d ⫹ z0 is identical and the diffusivities of water vapor and heat are close to each other (Fig. 1), it may be assumed that rc = r ⬘. Hence, introducing rc /ri = X and ri /ra = Y, (8) may be written as follows: t=

⌬ ⫹ ␥Y X 2Y D ⌬ ⫹ ␥ ⌬ ⫹ ␥ ⫹ ␥XY

(10)

which gives the relationship between temperature difference t and the atmospheric vapor pressure deficit D. Eq. (10), in fact, shows what should be an increase in temperature within the elements of the vegetated surface to ensure an actual latent heat flux ␭ET under potential atmospheric conditions ␭ETp defined by (1). Eq. (10) may be rearranged with respect to X and expressed in the following form: aX 2 ⫹ bX ⫹ c = 0

(11)

where a=

⌬ ⫹ ␥Y YD ⌬⫹␥

(12a)

b = ⫺␥Yt

(12b)

c = ⫺(⌬ ⫹ ␥)t

(12c)

Eq. (11) has only one positive solution corresponding to the ratio between the canopy and the climatological resistances, provided that the value of t is known. To determine t, the process of ET is described making use of the linear relationship assumption between saturation vapor pressure and temperature (Fig. 2). In the case of potential ET, water evaporates freely and the initial state of the unit volume of air with temperature T and vapor pressure ea is represented by point M. The adiabatic exchange of heat and water vapor brings the unit volume of air to point N, where it is saturated and cooler than it was initially by the temperature difference T ⫺ T1 . A complementary energy guided by a diabatic process, drawn mainly from the radiation, keeps the unit volume of air saturated on the path NQ. The efficiency of the total energy exchange determines the final position of the point Q. Because neutral atmospheric conditions are assumed in Fig. 2, the point Q es-

FIG. 2. Graphical Interpretation of Temperature Difference between Vegetated Evaporating Surface and Air above It for Potential and Actual State of Vegetation-Atmosphere System

timates the same temperature T as the initial point M, sensible heat flux is equal to zero, and all available energy is spent into evaporation. However, if ET originates within the vegetation elements, the process starts from some point M ⬘, which has a higher temperature T ⬘ than the air temperature T. In this case the ET process may be described as an adiabatic exchange of heat and water vapor from M ⬘ to N ⬘ and then it is drawn diabatically on the path of the saturation vapor pressure versus temperature curve. The final position of the unit volume of saturated particles is determined by point Q ⬘ because the total energy available for ET remains unchanged. However, this energy is partitioned between the energy effectively used for ET—the section M ⬘P ⬘—and the energy used for heating the evaporating surface from T to T ⬘, which in Fig. 2 corresponds to the section PM ⬘. As an adiabatic exchange of heat and water vapor initially pushes the evaporating process, then only the diabatic part of the energy may be used for an additional heating of an evaporating surface. Because that additional heating causes a corresponding adiabatic decrease of the latent heat flux, it may then be assumed that the most probable increase of temperature on the route NQ is that providing the difference in the vapor pressure ⌬D/(⌬ ⫹ ␥). As the route NQ is on the slope of the saturated vapor pressure versus temperature curve, then the predicted temperature of evaporating surface T ⬘ is greater than that of the air for the value t=

␥ D ⌬ (⌬ ⫹ ␥)

(13)

Eq. (13) describes the temperature difference between an evaporating surface with rc = 0 and rc > 0 as a function of the climatic variables (air vapor pressure deficit and air temperature) determined at one level above the canopy. Hence, an estimate of actual ET rate from a vegetated sur-

FIG. 3.

Flow Chart of Model for ET Estimate

JOURNAL OF IRRIGATION AND DRAINAGE ENGINEERING / SEPTEMBER/OCTOBER 1999 / 237

face follows the procedure illustrated in Fig. 3. This procedure is used for the testing of the ET model on an hourly and daily basis. MATERIALS AND METHODS The model was validated using the weather and lysimeter data from grass measured on an hourly basis at Davis (California) and on a daily basis at Policoro (southern Italy). Data Set for Model Validation on Hourly Basis (Davis, Calif.) The flux, climatic, and lysimeter data obtained at Davis, Calif., are those published by Pruitt and Lourence (1965). The experimental site is characterized with the semiarid Mediterranean climate with 38⬚32⬘ N, 121⬚46⬘ W, and altitude 18 m above sea level. The very sensitive weighing lysimeter covered by perennial ryegrass (Lolium perenne, L.) was used for ET measurements. The grass was maintained under optimal water conditions. The average height of grass during the measurements was not lower than 10 cm. Moreover, the measurement of fluxes, based on the aerodynamic, energy balance, and combination techniques was carried out. The lysimeter was a large circular area of 6.1 m in diameter and a depth of 0.97 m. It was equipped with soil temperature control and soil water suction control at the bottom. The resolution of the weighing system was within 0.03 mm of ET. The lysimeter site was irrigated frequently following each depletion of about 7.6 cm out of a total of about 15 cm of available water in the 90-cm soil profile. The procedures of obtaining net radiation, all of the other information relating to the corrections applied for the determination of data, and the approaches used for the flux determination have been discussed in a report of Pruitt and Lourence (1965). The data were taken from smoothed profiles (at heights of 25, 50, 100, and 200 cm) of temperature, humidity, and wind along with information for soil temperature at 1 cm depth below the soil surface of the lysimeter. Net radiation was measured by a forced-ventilated radiometer mounted at a height of 2 m above the grass canopy. Measured values of three of the energy balance components (net radiation flux, soil heat flux, and latent heat flux) were given along with the fourth (convective sensible heat flux) calculated as a remainder term. The available (published) data refer to half-hour information for the eight days of records during the years 1962 and 1963, covering all of the seasons except winter. Five out of eight days of measurements fall in the summer period. The average temperature ranged from 25 to 30⬚C during the summer days and on June 6th, and it was about 19⬚C on October 30th of 1962, and about 15⬚C on March 6th of 1963. The average relative humidity ranged from 30 to 50% for all days except October 30th of 1962, when it was about 65%. The average net radiation was the highest in June 6th of 1963 (around 0.56 KJ m⫺2 s⫺1) and July 31st of 1962 (around 0.37 KJ m⫺2 s⫺1); it varied for all other days between 0.23 and 0.29 KJ m⫺2 s⫺1. The average wind speed measured at a height of 2 m at Davis, Calif., was never below 1.2 m s⫺1 and it was extremely high for July 30, 1962, March 12, 1963, and June 6, 1963 (4.0, 7.1, and 5.8, m s⫺1, respectively). In fact, Pruitt and Lourence (1965) indicated the occurrence of high advection for March 12th and June 6th of 1963. Data Set for Model Validation on Daily Basis (Policoro, Southern Italy) The Policoro data set represents daily lysimeter and weather data collected at the experimental field ‘‘E. Pantanelli’’ of

Bari University, located in the area of Policoro (Province of Matera), along the Western Ionian Coast, about 3 km from the sea. The altitude of the experimental site is 15 m above sea level, while the latitude is 40⬚17⬘ N and the longitude is 16⬚40⬘ E. The area of Policoro has a Mediterranean semiarid climate, characterized by the following long-term average values of the major climatic parameters: (1) minimum and maximum daily air temperature are 11.0 and 21.4⬚C, respectively; (2) minimum and maximum daily air humidity are 52 and 87%, respectively; (3) average wind speed is 2.3 m s⫺1; (4) eliophany is 6 h 36 min; and (5) average Class A pan evaporation is 5.2 mm day⫺1. Annual precipitation averages 567 mm, 29% of which is distributed from April to September. The agro-meteorological station was equipped with a Class A evaporimeter and 2 ⫻ 2 m wide and 1.3 m deep highprecision weighing lysimeter. The lysimeter was centered in a 60 ⫻ 60 m surface cropped with a fescue (Festuca arundinacea L.), a cool-season grass suited for reference ET measurements. The lysimeter site and the surrounding fescuecropped area were maintained with adequate levels of soil moisture and clipped periodically to keep the height between 8 and 15 cm. Irrigation was applied by sprinklers with a frequency from 3 to 5 days. The various sensors and instruments for the measurements of weather variables were located within the same grass cropped surface, although about 30 m from the lysimeter. The measurements of air temperature and relative humidity were taken, respectively, through a bimetallic thermograph and a hair hydrograph placed within the standard weather shelter at 2 m height above the ground. The wind speed was measured with a propeller anemograph 3.5 m above the grass surface. Bright sunshine duration was measured by a classical Campbell-Stokes sunshine recorder, whereas precipitation was estimated by a mechanical paper-recording rain gauge. The integrity of air temperature, relative humidity, and wind-speed data was assessed by comparison with a nearby station through ‘‘double mass analysis.’’ The data set, covering the information over seven years (1981–1987), was screened, applying quality criteria, which excluded from the analysis: (1) the days with rain and/or irrigation; (2) the days succeeding irrigation and/or rain greater than 10 mm; (3) the days of grass cuttings; and (4) the days when wind-speed records were below 0.5 m s⫺1, corresponding to the minimum threshold value of the anemograph. The data used in the analysis represent the information for 898 days, distributed over all seasons. Equations Used in Analysis The net radiation, aerodynamic resistance, and other parameters of the Penman-Monteith equation [(3)] are computed following the standard procedure suggested by Smith et al. (1991) and Allen et al. (1994b, 1998). In addition, the solar radiation data of Policoro were tested for accuracy using the solar radiation envelope curve, which indicates the maximum solar radiation that can occur on a given day. The consistent and uniform drift of solar radiation values above or below this curve may be used as an indication of the likelihood of improper functioning of the instrumentation for the determination of solar radiation. Allen et al. (1994b) and Allen (1996) proposed three methods for the correction of solar radiation. This analysis used the simplest Rso = (0.75 ⫹ 2 ⫻ 10⫺5Z )Ra

(14)

where Rso = solar radiation envelope curve; Ra = extraterrestrial radiation; and Z = station elevation (m). The solar radiation values calculated with the Angstrom formula from the measured bright sunshine hours were below the solar radiation

238 / JOURNAL OF IRRIGATION AND DRAINAGE ENGINEERING / SEPTEMBER/OCTOBER 1999

FIG. 4. Solar Radiation Calculated from Bright Sunshine Hours Rs 㛭 calc and Computed from Eq. (14) Rs 0 㛭 Allen versus Day of Year, Policoro, Southern Italy

FIG. 5. Solar Radiation Rs 㛭 corr Corrected as 1.11Rs 㛭 calc and Solar Radiation Computed from Eq. (14) Rs 0 㛭 Allen versus Day of Year, Policoro, Southern Italy

envelope curve computed by (14), which indicates rections should be performed (Fig. 4). Corrections radiation were made using the correction factor of the corrected values of solar radiation are plotted in

that corfor solar 1.11 and Fig. 5.

RESULTS AND DISCUSSION Model Validation on Hourly Basis The 30-min grass ET data estimated by the model ETmodel from Davis, Calif., were compared with the lysimeter values ETly , the values calculated by the Penman-Monteith P㛭 M equation using the constant rc of 70 s m⫺1 ET70 and the values obtained using the Bowen ratio technique ETBowen . The results of comparisons, presented in Fig. 6, show that the ET values estimated by the model are in the range of those obtained by the Bowen ratio technique and those using the constant rc of 70 s m⫺1 for most days. The overestimation of ETmodel during the morning hours on August 15, 1963, and for the first half of August 31, 1962, averaged from 10 to 15% deviation. Two days (March 12, 1963 and June 6, 1963), when the performances of ET70 were superior, were indicated by Pruitt and

Lourence (1965) as the days of advection and very high wind speed (the average wind speed was 7.1 and 5.8 m s⫺1, respectively). The 30-min ET data for ETly , ETmodel , and ET70 were summed on a daily basis and compared (Table 1). These results confirmed the excellent performance of ETmodel , which for most days (excluding the days of advection) showed slight deviations of ⫺3 to ⫹1% relative to the ET obtained by lysimeter. The values summed from the ET70 method, in general, slightly underestimate ETly . The canopy resistance estimated by the model rc 㛭 model and the canopy resistance calculated from the Penman-Monteith equation when ␭ET was set equal to the measured-lysimeter data rcP 㛭 M are plotted in Fig. 7. Despite the excellent agreement in the ET values, there is no significant convergence between the resistance values calculated by the model and those derived from the Penman-Monteith equation. In general, rc calculated from the Penman-Monteith approach, which should represent the real rc (i.e., the rc to be used in the Penman-Monteith equation to estimate ETly ), shows great variations from day to day and also within the same day. Some of this variation could be caused by day to day errors and biases in the lysimeter and

JOURNAL OF IRRIGATION AND DRAINAGE ENGINEERING / SEPTEMBER/OCTOBER 1999 / 239

FIG. 6. Comparison between Measured and Estimated ET mm h⫺1 from Grass with Model ETmodel, Bowen Ratio ETBowen, and with Constant rc of 70 s m⫺1 ET70

240 / JOURNAL OF IRRIGATION AND DRAINAGE ENGINEERING / SEPTEMBER/OCTOBER 1999

FIG. 7.

Canopy Resistance s m⫺1 Estimated by Model rc 㛭 model and Derived from P 㛭 M Equation rcP 㛭 M , Davis, Calif.

JOURNAL OF IRRIGATION AND DRAINAGE ENGINEERING / SEPTEMBER/OCTOBER 1999 / 241

TABLE 1. Daily ET Measured by Lysimeter, Estimated by Model and Calculated Using Constant rc = 70 s m⫺1

Date (1)

ETly (mm day⫺1) (2)

ETmodel (mm day⫺1) (3)

ET70 (mm day⫺1) (4)

ETmodel deviation (%) (5)

ET70a deviation (%) (6)

30/7/62 31/7/62 31/08/62 30/10/62 12/03/63b 06/06/63b 14/08/63 15/08/63

5.57 12.13 9.00 3.70 3.27 9.94 11.76 12.80

5.43 12.04 9.06 3.61 6.86 11.09 11.38 12.94

4.79 11.07 9.07 3.56 4.87 8.84 11.04 12.29

⫺1.92 1.14 0.68 ⫺2.56 110.15 11.59 ⫺3.23 1.12

⫺13.50 ⫺6.99 0.80 ⫺3.84 49.06 ⫺11.11 ⫺6.14 ⫺3.94

Additional testing of both models was done when daily ET values obtained by ETmodel and ET70 were summed and compared with the summed lysimeter values. Again, ETmodel and ETly show very close agreement (the values were 3,350 and 3,359 mm, respectively), whereas the summed value of ET70 is about 100 mm or 2.8% greater than the ET cumulated at the lysimeter site. To improve the ET estimate with the constant rc , the model using constant canopy resistance was calibrated by optimizing the rc with respect to the minimum standard error of estimate for the whole data set of Policoro as well as on a monthly basis. The calibration, done for the whole data set, indicated the constant rc value of 71 s m⫺1 as the best fit for the Policoro data set, which does not significantly improve the ET estimate relative to rc = 70 s m⫺1. However, this value confirmed the

Note: Data refer to summed 30-min information from grass at Davis, Calif. a Deviation is calculated using formula (ETmethod /ETly ⫺ 1)100. b Days with advection.

weather parameters measurements that are gathered into the rcP 㛭 M term. Moreover, rcP 㛭 M does not show its theoretically expected parabolic variation during the day. In general, when the canopy resistance is calculated by the model the rc values showed a much more regular parabolic tendency, and for most days resulted in an average value of 40 s m⫺1. Nevertheless, this demonstrates the validity of the approach presented here rather than its accuracy in estimating the canopy resistance term. In addition, this confirms that the error in rc does not have a great influence on the error in ET. Validation of Model on Daily Basis Daily ET values computed by the Penman-Monteith equation using the variable canopy resistance ETmodel and the constant value of 70 s m⫺1 ET70 were compared with measured daily lysimeter ET at Policoro. The results of comparison are presented graphically in Fig. 8, whereas a summary of regression analysis for both models is given in Table 2. Linear regression analysis was of the form ETmethod = ␣ ⫹ ␤ETly

(15)

where ETmethod = particular ET estimate method; ETly = lysimeter-measured ET; and ␣ and ␤ = interception and slope of regression equation, respectively. The calculation of all terms in the ET analysis was done on a 24-h time step. The model using variable canopy resistance provided better and more consistent agreement with the lysimeter data than did the model using the constant rc of 70 s m⫺1. Root-mean-square error of estimate (RMSE) for the model with variable canopy resistance is about 6.5% lower than when the estimate was done using the constant rc . The results of regression analysis that was not forced through the origin also indicated that the performance of ETmodel was superior with respect to ET70. The model with constant rc demonstrates a greater tendency to overpredict ETly at lower values and to underpredict it at higher lysimeter values compared with the model with variable canopy resistance. The test of y-intercept against 0 revealed that the y-intercept was significantly different from 0 for both methods, whereas the test of slope against 1 showed that the slope is not significantly different from 1 only for ETmodel at a 5% level of significance.

FIG. 8. Comparison of Measured versus Predicted Daily ET Values for Grass with ETmodel and ET70 at Policoro, Southern Italy

TABLE 2. RMSE in mm Day⫺1 and Results of Regression Analysis Performed versus Lysimeter Data for ET70 and ETmodel (Policoro, Southern Italy)

Model (1)

RMSE (mm day⫺1) (2)

ET70 ETmodel

0.653 0.613

Regression not Forced through Origin

r2 (3)

␤ (4)

␣ (5)

Testing of ␣ = 0, t␣ (6)

Testing of ␤ = 1, t␤ (7)

0.904 0.913

0.881 0.932

⫹0.548 ⫹0.242

13.33 5.87

2.89 1.64

Note: Number of observation is 898. 242 / JOURNAL OF IRRIGATION AND DRAINAGE ENGINEERING / SEPTEMBER/OCTOBER 1999

Tabular t Distribution Values 5% (8)

1% (9)

1.960 1.960

2.576 2.576

FIG. 9. Monthly Variation of Canopy Resistance: Constant Value Optimized on Monthly Basis rc 㛭 opt , rc Calculated by ETmodel and Averaged on Monthly Basis rc 㛭 model, and rc Calculated from Penman-Monteith Equation and Averaged on Monthly Basis rcP 㛭 M TABLE 3. Deviation of Monthly Optimized Constant Canopy Resistance (rc 㛭 opt) and Monthly Averaged rc Calculated by ETmodel (rc 㛭 model) from rc Calculated from Penman-Monteith Equation and Averaged on Monthly Basis (rcP 㛭 M)

Month (1)

rc 㛭 opt (s m⫺1) (2)

rc 㛭 model (s m⫺1) (3)

rcP 㛭 M (s m⫺1) (4)

January February March April May June July August September October November December

96 80 88 62 75 50 57 95 87 78 101 106

142 121 104 84 78 70 71 78 90 106 131 131

168 122 117 74 94 64 74 116 117 122 155 157

rc 㛭 opt rc 㛭 model deviation deviation (%) (%) (5) (6) ⫺42.86 ⫺34.43 ⫺24.79 ⫺16.22 ⫺20.21 ⫺21.88 ⫺22.97 ⫺18.10 ⫺25.64 ⫺36.07 ⫺34.84 ⫺32.48

⫺15.48 ⫺0.82 ⫺11.11 ⫹13.51 ⫺17.02 ⫹9.38 ⫺4.05 ⫺32.76 ⫺23.08 ⫺13.11 ⫺15.48 ⫺16.56

Note: Deviation is calculated using formula (rc 㛭 method /rcP 㛭 M ⫺ 1)100.

validity of the approach to use the constant canopy resistance of 70 s m⫺1 suggested by Allen et al. (1989). The use of constant canopy resistance optimized on a monthly basis provided much more consistent ET estimates than did the model with the constant rc of 70 s m⫺1. RMSE = 0.623 mm day⫺1 is improved by almost 5%, whereas in the case of regression not forced through the origin, r 2 is 0.91, slope is 0.92, and y-intercept is ⫹0.36. However, these results are still inferior with respect to those when the ETmodel with the variable canopy resistance was used. To investigate the behavior of rc throughout the seasons, the values of canopy resistance optimized on a monthly basis rc 㛭 opt and monthly averaged values of canopy resistance obtained by ETmodel , rc㛭 model , were compared with the monthly averaged rc values calculated from the Penman-Monteith equation when the measured lysimeter data were used for ␭ET, rcP 㛭 M . The results (Fig. 9 and Table 3) clearly demonstrate that canopy resistance depends highly on climate. The variation of the resistances during the year was very similar to the theoretically expected parabolic variation of canopy resistance during the day. However, this is more evident for rc 㛭 model and rcP 㛭 M than for monthly optimized constant rc values. This is most likely due to the fact that the first two resistances rc 㛭 model

and rcP 㛭 M present a ‘‘linear’’ averaging of all daily estimates, whereas the rc 㛭 opt is impacted by nonlinearity of the leastsquare fitting. The monthly averaged values of rc 㛭 model were very well coupled with those derived from the Penman-Monteith equation. The rc 㛭 model reached the minimum of 70 (in June) and 71 s m⫺1 (in July), whereas the maximum, obtained in January and December, was 141 and 131 s m⫺1, respectively. Similarly, the minimum values of rcP 㛭 M were observed in June (64 s m⫺1) and in July (74 s m⫺1), whereas the maximum values corresponded to January and December with 168 and 157 s m⫺1, respectively. In the case of the monthly optimized constant canopy resistance, the minimum values, obtained during June and July, were 50 and 57 s m⫺1, respectively, whereas in January and December the rc 㛭 opt reached the maximum of 96 and 106 s m⫺1, respectively. The analysis of deviations of rc 㛭 model and rc 㛭 opt from rcP 㛭 M (Table 3) showed that for most of the months, canopy resistance obtained from ETmodel provided a significantly lower deviation than the constant rc optimized on a monthly basis. The opposite was observed only in August when, in general, the rc values were excessively high and ET was significantly lower than in June and July. This may be explained mainly due to ‘‘clearer’’ days, higher wind speed, and lower relative humidity in late spring and early summer than that in late summer (August and September). CONCLUSIONS The ET model presented here relies on the use of variable canopy resistance, which is a function of the common climatic variables measured above the vegetation. The model introduces the impact of the temperature of the evaporating surface that differentiates between ␭ETp , where rc = 0 and ␭ET, where rc > 0. The model accounts for the difference in the latent heat fluxes between the potential and actual ET rate, assuming that it is caused by an additional sensible heat flux imposed to heat the vegetation surface to provide the extra energy required to move saturated air out of vegetation elements. The ETmodel predicts this additional sensible heat flux by an approximation of the temperature difference t, which includes vapor pressure deficit and air temperature measured at one level above the canopy. Then, the model calculates the resistance of the evaporating surface and finally estimates the actual (reference) ET rate. The process of developing the equations for the proposed model is completely explicit in terms of equations presented,

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although the method itself includes some theoretical speculations and assumptions. The ETmodel may be used in all situations when the FAO Penman-Monteith method with the constant canopy resistance is used. The results of the presented analyses and the developed equations support the use of the FAO Penman-Monteith equation in ET estimates, and they demonstrate themselves useful to the irrigation engineering community. The presented model performed well in the estimates of ET from grass under optimal water conditions, and, at least using the data sets presented in this work, it does not require any calibration. However, further testing of the model is required to assess its applicability for climatic conditions different than that of the Mediterranean. The approach presented here also should be examined for the estimation of ET from vegetation types that are different from clipped grass (e.g., alfalfa). Finally, the model with the variable canopy resistance should also be tested under nonoptimal water conditions. Although the testing of the presented model has shown some superiority in respect to the use of the well-known FAO Penman-Monteith approach with constant rc = 70 s m⫺1 (ET70), the results of this work indicated that ET70 has also provided reasonable estimates of the lysimeter ET under Mediterranean climatic conditions. Therefore, significant underestimation of ETly with ET70, observed in some previous analyses for arid and semiarid lysimeter sites in the Mediterranean region (Caliandro et al. 1990; Rana et al. 1994; Steduto et al. 1996), could be partially explained by the fact that the solar radiation data were not corrected for improper functioning as was done in this work. Furthermore, the FAO Penman-Monteith approach with constant rc remains particularly valid when the input weather variables are not high-quality data or in the cases of the advection, because the use of constant rc excluded the error in using low-quality input information for modeling the canopy resistance term. Finally, it is important to report that atmospheric conditions above well-watered vegetation guide the canopy response to the environment not only on an hourly, but also on a daily and monthly basis. This is clearly demonstrated in the case of the Policoro data set when a similar seasonal parabolic curve was observed for both the monthly optimized constant rc and the rc calculated by the model and averaged on a monthly basis. This further recommends the use of the Penman-Monteith equation with a variable canopy resistance for the estimation of ET. ACKNOWLEDGMENTS This work was made possible due to the financial and technical support provided by the International Centre for Advanced Mediterranean Agronomic Studies (CIHEAM)—the Mediterranean Agronomic Institute of Bari (MAI—Bari). The writer is particularly grateful toward Dr. Cosimo Lacirignola, the Director of the Bari Institute, and Prof. Atef Hamdy, Director of Research, for their generous support and encouragement. The valuable suggestions of Dr. Pasquale Steduto (CIHEAM/MAI—Bari, Italy), Dr. Richard L. Snyder (University of California, Davis), and the two anonymous reviewers are highly appreciated. The writer would like also to acknowledge and thank Prof. Angelo Caliandro and Prof. Pietro Rubino (University of Bari, Italy) for providing the agrometeorological data of Policoro.

APPENDIX.

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