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Modelling evapotranspiration from a barley field over the growing season
Agricultural and Forest Meteorology 91 (1998) 237±250
Modelling evapotranspiration from a barley ®eld over the growing season Tapio Tourula*, Martti Heikinheimo Finnish Meteorological Institute, P.O.B. 503, 00101 Helsinki, Finland Received 12 March 1997; received in revised form 19 February 1998; accepted 23 February 1998
Abstract This study tested a modi®ed version of the two-layer evaporation energy combination scheme of Shuttleworth±Wallace (S±W). The ®rst modi®cation was the application of a two-layer soil module, which included the soil surface resistance for evaporation and soil moisture in the rooting layer controlling the canopy resistance. Another modi®cation was the inclusion of the surface temperature in the calculation of the aerodynamic resistance. The surface temperature controls both the stability and the canopy resistance. The modelled total evapotranspiration was compared with evaporation calculated from the Bowenratio energy-balance technique over two growing seasons of a barley ®eld, which provided a wide range of canopy densities and variation of driving factors with rainy, dry, warm and cold periods. The S±W scheme result on a daily and hourly basis was generally in good agreement with the measured evapotranspiration. The largest deviation between the measured and simulated evaporation occurred in a late phase of the growing season with a yellow non-transpiring canopy and, after harvesting, with stubble. The simulated surface temperature was mainly within 2 K of direct measurements, both in bare soil and dense canopy situations. The study showed that the scheme is applicable for practical use, since the weather input parameters required are limited to those which are available as normal synoptic observations. # 1998 Elsevier Science B.V. All rights reserved. Keywords: Evapotranspiration; Modelling; Crop; Measurements
1. Introduction The estimation of total evaporation and its components using easily-measurable meteorological variables is of great importance e.g. in crop growth monitoring programs, or in many practical operations, such as irrigation scheduling for farmers. For applications where the vegetation can be treated as a single layer *Corresponding author. Tel.: 00358 919291; fax: 00358 919294103; e-mail: [email protected] 0168-1923/98/$19.00 # 1998 Elsevier Science B.V. All rights reserved. PII S0168-1923(98)00065-3
(`big leaf'), the Penman±Monteith (P±M) combination equation has proven useful; this is the case when the crop canopy is well-developed and its cover is closed (Monteith, 1965). Over the entire growing season, however, this approach faces complications due to the signi®cant seasonal changes of the vegetation cover, as well as the varying tillage of the soil. Recent theoretical development of the P±M concept has led to the compartment schemes in which soil surface evaporation and transpiration from the canopy are resolved separately (Shuttleworth and Wallace,
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1985, Choudhury and Monteith, 1988, Noilhan and Planton, 1989 and Kustas, 1990). The Shuttleworth±Wallace (S±W) scheme has been validated with ®eld measurements by several authors for different types of sites and canopies. LaFleur's and Rouse's (1990) site was a subarctic wetland sedge meadow: they found excellent agreement between the measured and calculated evaporation. The soil surface below the canopy was wet all the time, causing the soil evaporation to take place at the potential rate. The S±W scheme was used for arid conditions by Nichols (1992), who evaluated the scheme on semiarid rangeland, where the vegetation consisted of sparse shrubs without any vegetation sublayer. Nichols used the approach of Shuttleworth and Gurney (1990) in the determination of the mean canopy resistance, needing sophisticated measurements of canopy foliage and soil surface temperatures. The estimate of transpiration was reasonably good, but the result for the soil surface evaporation was less satisfactory, although it played a minor role in the total ¯ux, due to the very dry soil surface. Iritz et al. (1997) used the S±W scheme, in the same form as was used in this paper, for a cultivated willow stand. From these studies, one may conclude that the S±W type of approach is most useful in the assessment of evapotranspiration from vegetated surfaces. In our approach the object of interest was a barley ®eld; the period of investigation was extended over the whole growing season, ranging from pre-sowing, through the various phenological phases of the annual crop, up to post-harvesting. This provided a wide range of canopy densities, with a leaf area index varying between zero and four. The factors driving the energy ¯uxes varied between rainy and dry periods, leading to a signi®cant variation of the soil moisture within the rooting depth of the crop. The control of transpiration by soil moisture and soil surface evaporation was therefore considered as an equally important part of the scheme. Another aim was to develop the scheme in such a way that the water balance was included. The S±W scheme was tested against measurements of evapotranspiration made with the Bowen-ratio method over two summers at an agricultural site in southern Finland. The overall goal was to identify the number of necessary input parameters to the scheme, while still allowing its use in practical applications.
2. The model 2.1. Overview of the Shuttleworth±Wallace scheme The S±W scheme is one-dimensional and describes the energy partition of a sparse canopy. The basic assumption is that the water vapour ¯ux from the soil to the atmosphere can take place simultaneously from the soil surface as soil evaporation, through plants as transpiration and thirdly as evaporation of the intercepted water. Practically, the scheme consists of a mathematical formulation of the resistances that control the vapour ¯ow. The procedure used in this study is based on the work of Shuttleworth and Wallace (1985) and is not repeated here in so far as the equations are identical. The procedure is extended in terms of the soil surface and bulk canopy resistances, as well as in the calculation of the aerodynamic resistances. 2.2. Calculation of aerodynamic resistances The aerodynamic resistance, raa , for stable and unstable conditions was calculated with an analytical method suggested by Choudhury et al. (1986). The required input variables are the aerodynamic surface temperature, Ts, which is de®ned to prevail at the virtual source/sink level of sensible heat, the reference height temperature, Tz and the wind speed at the reference height, u. In our case the reference height z was 2 m above the soil surface. The stability functions for momentum and sensible heat M and H were considered to be equal and expressed as:
B ÿ B2 ÿ 4aC0:5 = 2a
(1)
where: a1
(2)
B ln z ÿ d=z0H 2 ln z ÿ d=z0M
(3)
C lnf z ÿ d=z0M g2
(4)
5 z ÿ dg T0 ÿ
Tz = Tz u2z
(5)
and as a ®nal result the resistance is given for unstable conditions by: zÿd zÿd a ÿ ln ÿ k2 u ra ln z0M z0H (6)
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where k is the von Karman constant. For stable conditions the resistance is given by: zÿd zÿd a ln k2 u 1 0:75 (7) ra ln z0M z0H The displacement height d and roughness lengths for momentum ¯ux, zM, sensible heat ¯ux, zH and latent heat ¯ux, zE, depend in the method of Choudhury et al. (1986) on the canopy height h as follows (Legg and Long, 1975 and Garratt, 1978) d 0:56h
(8)
zM 0:3 h ÿ d
(9)
zH zE zM =7
(10)
The aerodynamic surface temperature, Ts, was calculated with a method given by Lhomme (1992). This method requires the bulk surface resistance rsurf as an input parameter, which can be calculated from the canopy and soil surface resistances rsc and rss as follows: rsurf 1= 1=rsc 1=rss
(11)
The aerodynamic surface temperature, Ts, can be calculated by: Ts Tz !=cp Rn ÿ G ÿ != Dz = raa rsurf (12) where Dz is the vapour pressure de®cit of the air at the reference level z. ! is de®ned by: ! 1=1=r0
1=raa
= raa
rsurf
(13)
where r0 is: r0 cp =4"Tz3
(14)
and is the slope of the saturated vapour pressure curve determined at the temperature of the air Tz, " the emissivity of the surface (0.98) and the Stefan± Boltzmann constant. Because the aerodynamic resistance raa was needed for the calculation of the aerodynamic surface temperature, the calculation was iterated a few times to obtain the adjustment of raa and Ts to the prevailing stability conditions. Normally, the ®nal values for Ts and raa converged within two or three loops to a precision of one per cent. The initial values of the resistances were obtained using a direct method given by Shuttleworth and Wallace (1985). Furthermore,
239
because rsurf depends directly on the aerodynamic surface temperature and on the vapour pressure de®cit of the canopy air via the aerodynamic and canopy resistances, the whole scheme was iterated ®ve times at each time step. The aerodynamic resistance within the canopy, ras , was calculated, as in S±W, using the (K-) theory of an eddy diffusivity assumed to vary exponentially with height within the canopy. Similarity between momentum, sensible heat and vapour transfer, as well as neutral strati®cation, were assumed. The value of ras was leaf-area-dependent, as given in the S±W scheme. It varied linearly between the asymptotic limits of a bare soil situation and a full canopy cover. The magnitude of rac , which controls transfer between the surface of the vegetation and the canopy air, was considered to be small compared to other resistances and a constant value of 5 s/m was used (Smith et al., 1988). Compared to the original S±W scheme, the main difference was that the stability effect was included in raa . On the other hand, no leaf area dependency is taken into account when calculating raa as was made in the original S±W scheme. This simpli®cation should play only a minor numerical role because, according to the sensitivity analysis of Shuttleworth and Wallace (1985), extreme changes in the original parameterization of raa and ras have less than a 5% effect on the total evaporation rate. 2.3. Calculation of canopy resistance To get an independent estimate of the canopy resistance, rM, the original Penman±Monteith equation was inverted (Eq. (15)) and solved for the surface resistance. A two-week test period (starting 1 July 1991) was selected for which the crop canopy was fully-developed (leaf area index>3) and closed. Under such conditions the evaporation from the soil through the canopy was assumed to be small and hence the calculated surface resistance closely approximated the canopy resistance rsc . raa Rn ÿ G cp es ÿ e0 =raa rM ÿ
Etot (15) where cp is the heat capacity of air, es the saturated and e0 the ambient vapour pressure at a reference
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height, the psychometric constant, Rn the net radiation and G the soil heat ¯ux. To determine the value of the minimum canopy resistance, rsmin , 5 cases, lasting a few hours on separate days during the two week test period, were found having minimum limitations by the environment. The soil moisture was near ®eld capacity, the temperature was between 178C and 258C, the vapour pressure de®cit at the 2 m level was below 5 hPa and the global radiation was over 400 W mÿ2. It was assumed that the stomata were fully open during these optimal conditions and that the surface resistance rsc , calculated from (Eq. (15)), represented its minimum value rsmin . To correct the value for the effect of the shading of leaves deeper in the canopy, rsmin was divided by a constant A, which was calculated by the method based on Noilhan and Planton (1989). A
1f f rsmin =rsmax
(16)
where: f 0:55Rn =L
(17)
where L is the leaf area index of green and yellow leaves. For the barley crop, we obtained an average value of 90 s/m with a variation of 40 s/m. Previously, KoÈrner et al. (1979) has reported corresponding values ranging from 90 to 100 s/m. It is emphasised that these values are not bulk values for the whole canopy but are mean values per unit area of Green Area Index, LG (1 m2). The canopy resistance was parameterized according to the method given by Avissar et al. (1985) as a multiplicative response to several environmental factors expressed as F1 ; . . . ; F4 . rsc rsmin = F1 F2 F3 F4 LG
(18)
where rsmin represents the minimum resistance with fully open stomata and LG is the total green area contributing to transpiration. The use of LG allows the use of this parameterization throughout the whole growing season, because only the transpirating partition of the leaves is taken into account. The functions F1 ; . . . ; F4 in (Eq. (18)) refer to the in¯uence of global radiation (F1), leaf temperature (F2), within-canopy vapour pressure de®cit (F3) and plant-available soil moisture content (F4), respec-
tively. All F-functions have the same general form: Fi 1=f1 expÿS Xi ÿ bg
(19)
where the subscript i refers to the environmental factors, whose values are given by Xi. S and b are species-speci®c constants. The values of the F-functions can vary between 0 and 1, with 0 indicating full closure of the stomata and 1 fully-open stomata. In the case where one or more of the F-functions reach zero, the value of (Eq. (18)) becomes unde®ned and rsc is given a maximum value of 50 000 s/m. This corresponds to the molecular diffusivity of water vapour transfer through leaf cuticula. Due to the lack of global radiation measurements, we used twice the value of the net radiation as an estimate for it. This should not much affect the result, because during daytime the amount of radiation was not a limiting factor. The role of radiation was mainly to act like a switch, which turned off the evaporation during the night time. The leaf temperature was assumed to be identical to the aerodynamic surface temperature Ts, which was calculated by (Eq. (12)). The vapour pressure de®cit of the canopy air, D0, was obtained as in the original S±W scheme. The method was calibrated against the measured evapotranspiration in a two-week period (starting 1 July 1991). The parameters S and b given in Table 1 were adjusted, keeping in mind that they should differ as little as possible from the physical values determined by the measurements for similar species (Kueppers, 1988 and Turner, 1991). The parameter set was a compromise between the optimal mathematical solution and physically reasonable values. When varying the parameters around their given values, any signi®cant improvement in the modelled transpiration on a daily basis was not found. Table 1 Parameters used in the Avissar scheme for the bulk canopy resistance Parameter Global rad. Leaf temperature Vapour pressure deficit Soil moisture
Units ÿ2
Wm K Pa Vol.%
S
b
0.03 0.41 ÿ0.003 3000
40 280 700 25
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2.4. Calculation of the soil surface resistance The resistance to moisture transfer from the soil, rss , was calculated using a hypothetical two-layer parameterization proposed by Choudhury and Monteith (1988). The upper hypothetical dry layer l1 increases in depth as the soil evaporation Esoil takes place and decreases as it rains, P, in accordance with Eq. (20). 2 is the volumetric soil moisture of the lower layer, l2, reaching down to the rooting depth. @l1 Esoil ÿ P=2 @t
(20)
The lower soil layer, l2, is moist. The evaporation from the soil is assumed to originate from the top of that layer. The soil surface resistance, rss is kept at zero until l1 reaches 0.2 mm. After that threshold, rss increases in proportion to l1 according to the following relation: rss
ÿ5
1:41 10 l1
(21)
The total volumetric moisture content, tot, from the soil surface down to depth l2 is used for the calculation of the canopy resistance. This value differs by just a few percent from 2, which is the volumetric moisture of the lower layer only and was calculated with a simple bucket method. The soil moisture 2 is only reduced by uptake by the plant roots i.e. transpiration, Etrans and increases by supply from in®ltrated rain water, Pinf. @2 1 Pinf ÿ Etrans @t w l 2
(22)
where t is time and w is the density of water. The upwelling of moisture from ground water is assumed to be negligible, due to the clay soil composition and the presence of underground drainage channels. During rain, droplets ®rst fall on the leaves and the interception storage is ®lled. The remaining water is then used to wet the 0.2 mm deep buffer at the soil surface, after which the upper dry layer l1 starts to ®ll, but only up to moisture 2. Filling the upper layer is performed according to Eq. (20) i.e. the depth of the layer decreases. Upon ®lling, i.e. the vanishing of l1, the whole soil layer from the surface to depth l2 attains the original moisture 2. If the rain still continues, 2 increases according to Eq. (22) up to ®eld capacity, after which runoff takes place.
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2.5. Calculation of the evaporation of intercepted water The evaporation of the intercepted water, Eint, was calculated by the method suggested by Noilhan and Planton (1989) cp Wfr es ÿ e0 =raa (23) Eint
where Wfr is a power function of the moisture content of the interception reservoir, calculated as proposed by Deardorff (1978): Wr 2=3 (24) Wfr Wrmax where Wr is the actual amount of intercepted water and Wrmax is the maximal possible amount de®ned by Dickinson (1984): Wrmax 0:2L
(25)
where L is the leaf area index of green and yellow leaves. 3. Measurements Measurements were carried out on a non-irrigated barley ®eld (Hordeum vulgare) in Southern Finland (608250 N latitude, 248240 E, longitude, 47 m altitude). The soil texture was sandy clay and the ®eld sloped gently to the north-east. The ®eld contained underground drainage channels at a depth of about 1 m. The fetch of open homogeneous ®eld from the surrounding coniferous forest boundary was 300±1000 m depending on the wind direction. For this study we used data sets from the summers of 1991 and 1992. In 1991 the 125-day period began on 20 May and ended on 31 August. In 1992 the ®rst day of the measurements was 20 May and the last 18 August. These two summers differed signi®cantly in terms of precipitation. Summer 1991 was more or less normal with alternating dry and rainy periods and a well-developed crop canopy. Mean temperature and wind speed were close to normal long-term values. The ®rst half of summer 1992 was extremely dry, with the consequence that severe drought hindered the development of the crop canopy. The leaf area index reached a value of 1, being about 50% smaller than in
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Fig. 1. Seasonal variation of green leaf area index (LLG), total green area index (LG) and canopy height (hc) in 1991 and 1992.
1991. In July and August the weather was normal with rainy periods. Evapotranspiration, Emeas, was estimated by the Bowen-ratio method (the instrumental set-up was that commercially available from Campbell Science, UK), using a 20 min averaging period. The distance between the lower and the upper vapour pressure and temperature measurement levels was 1 m. The lower level was kept at approximately 1 m above the soil/top of the canopy. Net radiation was measured with a Fritschen-type (Q5, Campbell Science, UK) domed radiometer. In addition, air temperature, relative humidity and wind speed were measured at a ®xed 2.2 m level above the soil surface. Occurrences of rain or dew were monitored with a wetness sensor (Model 237, Campbell Science). For certain periods, the radiative skin temperature of the foliage was measured with an instrument manufactured by Everest Interscience (model 4000, angle of view 158). The instrument was placed at a height of 2.5 m and was pointed eastward, tilted 208 below the horizon. An internal checking routine was developed to evaluate the measured variables and to clearly mark erroneous values. Periods of bad data were excluded
from the summing of the daily totals. Daily totals of ¯ux quantities were calculated for the whole 24 h period. Daily means of other quantities, i.e. canopy and soil resistances, were calculated for the daytime, between 09±18 h local time. Daily precipitation was obtained partly from a nearby climatological station located 2 km east of the site. The daily amounts of precipitation were split into 20 min values based on the information from the wetness sensor and assuming a constant rainfall intensity. Temporarily, the precipitation was measured at the site using a tipping-bucket-type rain gauge. Such periods were from 1 July to 15 August in 1991 and from 27 May to 3 July in 1992. When this data was available, it was used in the calculations. In 1992 the soil moisture was measured about once a week with a neutron probe at one point in the ®eld close to the other instruments. An estimate of the crop's phytometric properties was obtained by the periodic destructive sampling throughout the life cycle of the crop. The measured quantities were: leaf area index, L, of green and yellow leaves, leaf area index of green leaves only, LLG, stem green area index, LSG and height of canopy, hc. The
T. Tourula, M. Heikinheimo / Agricultural and Forest Meteorology 91 (1998) 237±250
total green area index, LG, was de®ned as follows: LG LLG 0:5LSG
(26)
The factor 0.5 takes into account the fact that on the surface of stems the density of stomatal pores is sparser than on leaves. All areas were expressed per unit ground area, Fig. 1 and the curves presented are ®tted to measured points. The development of plant roots was estimated assuming a sowing depth of 5 cm and using the root growing rates and rooting depths measured by Ilola et al. (1988) for a similar soil type and climate conditions. The maximum rooting depth was set somewhat arbitrarily at 50 cm in 1991 and at 25 cm in 1992. 4. Results 4.1. Surface temperature as the scheme output The surface temperature is a key parameter for the aerodynamic resistance, because it largely determines the stability of the surface layer. In dense canopies, foliage surface temperature serves as a ®rst order estimate of the temperature of the transpiring leaves, which controls transpiration through the canopy resistance. For interpreting the modelled results it was important to estimate how well the calculated aerodynamic surface temperature, Ts, agreed with the measured one, Tsm. Two weeks were selected for evaluation. During the week starting 18 May 1992 the soil was completely bare and freshly tilled due to sowing carried out just a few days before (Fig. 2(a)). During the week starting 1 July 1991 the barley canopy was fully developed with an LG>3 (Fig. 2(b)). The ®rst day of the week starting 18 May 1992 was mainly sunny, with a relatively high surface temperature. Around mid-day the calculated temperature was about 58 lower than that measured. One probable reason for this was the orientation of the IR-sensor towards the east, thus causing the warmer side of the soil granules to face the sensor. The estimation of the soil heat ¯ux could also have been unrepresentative due to the strong moisture gradient at the surface and the large horizontal variability of moisture and other soil properties. Over the following ®ve, mostly cloudy, days the deviation was smaller, within the limits
243
of 28. The last day was again partly sunny with somewhat larger deviations. In conclusion, it can be stated that in bare soil conditions the model is able to handle cloudy days better than sunny days with an extremely high surface temperature compared to the air temperature. The assumption of the same roughness length of heat to momentum ratio (zH/zM) for bare soil as for a dense canopy may partly explain the deviation. The period before the week starting 1 July 1991 was rainy. The ®rst three days of the week starting 1 July 1991 were cloudy, with a little rain occurring on the ®rst and third days. The last four days were mainly sunny and warm. The overall agreement during the week was good, considering the large daily variability of actual and calculated temperatures. Though the diurnal amplitude of the calculated temperature tended to be smaller, the deviation remained mainly within 28. A small time shift was also seen, i.e. during the mornings the calculated temperature rose slightly earlier and in the evenings fell somewhat earlier. One possible cause for the deviation in a dense canopy situation could be that the calculated value represented the source level of the sensible heat ¯ux rather than the top of the canopy seen by the IR-sensor (Choudhury et al., 1986). Despite the temporal discrepancies between the measured and calculated surface temperatures the overall correspondence was good giving con®dence to the calculation of the aerodynamic resistance and canopy resistance. Similar conclusions have been reported e.g. by Smith et al. (1988). 4.2. The behaviour of the vapour pressure deficit within the canopy The vapour pressure de®cit within the canopy, D0, is an important parameter, because it controls transpiration through its in¯uence on stomatal resistance. Two contrasting periods were selected to assess the magnitude of this effect. On the week starting 8 June 1991 the canopy was very sparse, with an LG of about 0.4 (Fig. 3(a)). The behaviour of D0 showed features similar to what one would expect for bare soil conditions, where the solar radiation strongly heats the soil surface, causing a large difference between the temperatures at the reference and the canopy/soil levels. The temperature difference is clearly illustrated
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Fig. 2. Comparison of the calculated surface temperature (Ts), measured surface temperature (Tsm) and measured air temperature (Tz), (a) for bare soil conditions during the week beginning 18 May 1992; (b) for closed canopy conditions during the week beginning 1 July 1991.
T. Tourula, M. Heikinheimo / Agricultural and Forest Meteorology 91 (1998) 237±250
245
Fig. 3. Simulated canopy level vapour pressure deficit (D0) compared to measured reference level vapour pressure deficit (Dz), (a) for sparse canopy conditions during the week beginning 8 June 1991; (b) for closed canopy conditions during the week beginning 1 July 1991.
in Fig. 2(a). The in¯uence of D0 on the calculated evapotranspiration is negligible, due to the minor role of transpiration in this situation.
During the week starting 1 July 1991, with a dense canopy, the values of D0 were smaller and close to the vapour pressure de®cit at the reference level, Dz
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(Fig. 3(b). D0 increased during the morning hours above Dz, but decreased below Dz in the afternoon, when transpiration moistened the canopy air. It is to be pointed out that D0 and the bulk canopy resistance are not independent variables. There is strong positive feedback: when the canopy resistance decreases, transpiration increases, leading to a decreasing D0, which in turn causes a further decrease in the canopy resistance.
By studying some sub-periods of the simulation, some noteworthy points can be discovered. It can clearly be seen that the magnitude of the soil evaporation is highly dependent on the canopy density. With a dense canopy at the beginning of July 1991, the soil evaporation did not exceed 15% of the total ¯ux, even in the case of a wet soil surface. At the end of June 1992, with a sparse canopy and wet soil surface conditions, the proportion of the soil evaporation reached a maximum of 28%. The day-to-day variability of evapotranspiration was large, but it was well-simulated for most of the time. This indicates that the mechanisms regulating transpiration were rather well covered by the present parameterization. At the beginning of summer 1992, Bowen-ratio measurements were started immediately after cultivation and sowing, when the soil was still completely bare. This provided the possibility of verifying the calculated soil surface evaporation against measurements. The daily evaporation amounts were low due to the dry spell (Fig. 4(a)). During the dry period the soil surface resistance continuously increased, but daily evaporation was still rather well simulated. The evaporation of the intercepted rain water was also included in Fig. 4. It improved the result in most cases, but in some cases it made them poorer, however. When L was large, the in¯uence was clearly positive, as seen on e.g. 29 June 1991. Later, in August, the interception part improved the result during some periods, when the canopy was yellow and hence the
4.3. Simulations of the total evapotranspiration The simulations of total evapotranspiration were made for two full growing cycles of barley in 1991 and 1992. The seasons differed from each other, which is indicated for example by the maximum LG (see Fig. 1), resulting in a signi®cant difference in the levels of the evapotranspiration (see Fig. 4). The seasonal sum of the total evapotranspiration Etot (the sum of soil surface evaporation, Esoil, transpiration, Etrans and evaporation of intercepted water, Eint) differed signi®cantly from summer 1991 to summer 1992, being in reasonable agreement with the measured evapotranspiration in both years (Table 2 and Fig. 4), indicating that the separate terms of the simulated evapotranspiration were of realistic magnitude. Signi®cant discrepancies arose under conditions of mature crop and stubble in August and September 1991, as illustrated in Table 2(a).
Table 2 Cumulative precipitation and evaporation for selected sub-periods in (a) 1991 and (b) 1992 (a) 1991 P Eint Esoil Etrans Etot Emeas
[mm] [mm] [mm] [mm] [mm] [mm]
20±31 May 9 0 7 0 7 ±
1±30 June
1±31 July
1±31 August
70 6 22 22 50 ±
18 5 12 60 77 80
181 10 21 3 34 50 1±18 August
(b) 1992
18±31 May
1±30 June
1±31 July
P Eint Esoil
0 0 7 1 8 10
11 2 9 30 41 39
30 6 16 19 41 39
trans
Etot Emeas
[mm] [mm] [mm] [mm] [mm] [mm]
51 2 15 1 18 17
1±21 September 23 4 9 0 13 27 18 May±18 Aug. 92 10 47 51 108 105
20 May± 21 September
1 July± 21 September
301 25 71 85 181 ±
222 19 42 63 124 157
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247
Fig. 4. Comparison of the calculated daily total evapotranspiration (upper thin line) to the measured values (thick line) obtained by Bowenratio method for the growing seasons in 1991 (a) and 1992 (b). The shaded areas correspond to the estimated components of total evapotranspiration: transpiration (Etrans), soil evaporation (Esoil) and evaporation of intercepted rainfall (Eint).
transpiration was small. On a hourly basis the function of the interception part varied due to the unrepresentative precipitation measurement. This is illustrated in
Fig. 4 on some isolated days where the simulated result clearly exceeded the measured value. The evaporation of intercepted water in accumulated amounts
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as a fraction of the total evapotranspiration in 1991 was 14% while it was 9% in 1992, emphasising the importance of this part. The evaporation of intercepted water could exceed about 50% of the total budget of the total daily evapotranspiration, especially on rainy days of a shower type. There were two sub-periods during summer 1991 in which a relatively large discrepancy between the calculated and measured evaporation occurred. The ®rst was when the crop had reached its maturity and the green part of the canopy was decreasing rapidly. During this period the estimation of the LG (Green Area Index), i.e. the area of the transpiring surface of the canopy, was very dif®cult. The second period of discrepancy was found after harvesting, i.e. when the ®eld was covered with 15 cm tall stubble and straw, whose characteristics were dif®cult to parameterize. The albedo, the isolation of the soil surface by the surface residue and interception are all factors which may have caused possible inaccuracy in the result. One aim was to introduce soil moisture into the scheme. The method was in essence simple, but realistic. The curves of volumetric soil moisture calculated for the soil layer from the surface to the rooting depth are plotted in Fig. 5 . Unfortunately the corresponding weekly measurements were only available for 1992. In 1991, the initial pro®le of soil moisture was set at ®eld capacity, because after the melting of the snow there was enough water available. In 1992, measurements provided the initial value for the soil moisture. It is to be noted that the soil moisture measurements were only made at one point and were probably not fully representative of the whole ®eld. This may partly explain the differences between the measured and modelled moistures. However, the overall agreement was good and the shape of the modelled moisture followed the trend of the measured points nicely. This gives con®dence in the simple approach used here, in which the soil moisture budget does not contain in®ltration to ground water or percolation. The daily precipitation is also shown as columns and the signi®cant difference between the two seasons is clearly seen. The soil surface resistance, rss , rapidly increased as the soil dried. When precipitation reached the soil surface so as to wet it, rss dropped to zero. However, since small amounts of water intercepted at the soil surface are soon evapo-
rated back into the air, rss rose rapidly to close to its previous level. 5. Conclusions By using a simple two-layer scheme for evapotranspiration, it was possible to estimate the actual total evaporation with an accuracy that is considered suf®cient for practical applications. The water balance of a crop ®eld, at least in the case of a simple uniform soil texture, could be estimated using a simple bucket-type two-layer soil parameterization. This kind of resistance network parameterization allows one to study the sub-processes of water transport from the soil to the atmosphere separately. One of the important factors controlling the ¯ux was found to be the surface temperature, affecting both the aerodynamic and canopy resistance. The vapour pressure de®cit of the canopy layer was also important, controlling the evaporation demand and canopy resistance. In our approach the calculation scheme was kept as general as possible, allowing easy adaptability to different kind of sites with varying vegetation and soil properties. The aerodynamic resistance does not need sophisticated measured parameters, such as the canopy surface temperature or wind pro®le. Nevertheless the canopy resistance, another signi®cant term in the water transport of vegetated sites, is easy to adjust for different vegetation, since the parameterization includes four separate factors. The input variables required were restricted to those which are available directly or are able to be calculated from synoptic observations. Temperature, humidity and wind speed are directly available. A dif®cult variable to handle in this respect is the precipitation, for which at least hourly values are required. Some algorithms do exist to create hourly precipitation data from measurements made every 12 h (Lystad and Tallaksen, 1991). The available energy (RnÿG) is a variable which is not measured at normal synoptic stations. There are methods by which it is possible to estimate global radiation using observations of cloudiness and net radiation (VenaÈlaÈinen and Heikinheimo, 1996). Taking all the previous points into account, it would be possible to use the scheme based purely on synoptic data, without any sophisticated micrometeorological measurements.
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249
Fig. 5. Comparison of the daily means of the measured and modelled soild moisture of the rooting layer (meas and tot) shown with the corresponding soil surface resistance (rss ) and precipitation (P) for (a) 1991 and (b) 1992.
This opens a broad perspective for practical applications, such as the real-time monitoring of soil moisture for large agricultural areas e.g. for purposes of irriga-
tion scheduling, or the monitoring of forest evapotranspiration for hydrological applications. For these kinds of large-scale simulation the canopy properties
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required, i.e. LAI and height, could be obtained from satellite monitoring using the NVDI-index or by using the predetermined phenological schemes for different vegetation covers. References Avissar, R., Avissar, P., Mahrer, Y., Bravdo, B.A., 1985. A model to simulate responses of plant stomata to environmental conditions. Agric. For. Meteor. 34, 21±29. Choudhury, B.J., Monteith, J.L., 1988. A four-layer model for the heat budget of homogeneous land surfaces. Quart. J. R. Meteor. Soc. 144, 373±398. Choudhury, B.J., Reginato, R.J., Idso, S.B., 1986. An analysis of infrared temperature observations over wheat and calculation of latent heat flux. Agric. For. Meteor. 37, 75±88. Deardorff, J.W., 1978. Efficient prediction of ground surface temperature and moisture with a inclusion of a layer of vegetation. J. Geophys. Res. 83(4), 1889±1903. Dickinson, R.E., 1984. Modeling evapotranspiration for three dimensional global climate models. Climate processes and climate sensivity. Geophys. Monogr. 29, 58±72. Garratt, J.R., 1978. Transfer characteristics for a heterogeneous surface of large aerodynamic roughness. Quart. J. R. Meteor. Soc. 104, 491±502. Ilola, A., Elomaa, E., Pulli, S., 1988. Testing of Danish growth model for barley, turnip rape and timothy in Finnish conditions. J. Agric. Sci. Finland 60, 631±660. Iritz, Z., Tourula, T.A., Lindroth, Heikinheimo, M., 1997. Simulation of willow short rotation forest evaporation using a modified Shuttleworth±Wallace approach, Submitted to Journal of Hydrology. Kueppers, M., 1988. Water vapour and carbon dioxide exchange of leaves as affected by different environmental conditions. Acta Hortic. 229, 85±112. Kustas, W.P., 1990. Estimations of evapotranspiration with oneand two-dimensional model of heat transfer over partial canopy cover. J. Appl. Meteorol. 29, 704±715.
KoÈrner, C., Scheel, J.A., Bauer, H., 1979. Maximum leaf diffusive conductance in vascular plants. Photosynthetica 13, 45±82. LaFleur, P.M., Rouse, W.R., 1990. Application of an energy combination model for evaporation from sparse canopies. Agric. For. Meteor. 49, 135±153. Legg, B.J., Long, I.F., 1975. Turbulent diffusion within wheat canopy. II: Results and interpretation. Quart. J. R. Meteor. Soc. 101, 611±628. Lhomme, J.P., 1992. Energy balance of heterogeneous terrain: Averaging the controlling parameters. Agric. For. Meteor. 61, 11±21. Lystad, S., Tallaksen, L., 1991. Simulert timesfordeling av nedboÈr, DNMI Klima Report, 26. Monteith, J.L., 1965. Evaporation and the environment. Symp. Soc. Exp. Biol. 19, 205±234. Nichols, W.D., 1992. Energy budgets and resistances to energy transport in sparsely vegetated rangeland. Agric. For. Meteor. 60, 221±247. Noilhan, J., Planton, S., 1989. A simple paramerization of land surface processes for meteorological models. Mon. Wea. Rev. 117, 536±549. Shuttleworth, J.W., Gurney, R.J., 1990. The theoretical relationship between foliage temperature and canopy resistance in sparse crops. Quart. J. R. Meteor. Soc. 116, 497±519. Shuttleworth, W.J., Wallace, J.S., 1985. Evaporation from sparse crops ± an energy combination theory. Quart. J.R. Meteor. Soc. 111, 839±855. Smith, R.C.G., Barrs, H.D., Fisher, R.A., 1988. Inferring stomatal resistance of sparse crops from infrared measurements of foliage temperature. Agric. For. Meteor. 42, 183±196. Turner, N.C., 1991. Measurement and influence of environmental and plant factors on stomatal conductance in the field. Agric. For. Meteor. 54, 137±154. VenaÈlaÈinen, A., Heikinheimo, M., 1996. The spatial variation of long-term mean global radiation in Finland. Int. J. Clim., in press.
Modelling evapotranspiration from a barley ®eld over the growing season Tapio Tourula*, Martti Heikinheimo Finnish Meteorological Institute, P.O.B. 503, 00101 Helsinki, Finland Received 12 March 1997; received in revised form 19 February 1998; accepted 23 February 1998
Abstract This study tested a modi®ed version of the two-layer evaporation energy combination scheme of Shuttleworth±Wallace (S±W). The ®rst modi®cation was the application of a two-layer soil module, which included the soil surface resistance for evaporation and soil moisture in the rooting layer controlling the canopy resistance. Another modi®cation was the inclusion of the surface temperature in the calculation of the aerodynamic resistance. The surface temperature controls both the stability and the canopy resistance. The modelled total evapotranspiration was compared with evaporation calculated from the Bowenratio energy-balance technique over two growing seasons of a barley ®eld, which provided a wide range of canopy densities and variation of driving factors with rainy, dry, warm and cold periods. The S±W scheme result on a daily and hourly basis was generally in good agreement with the measured evapotranspiration. The largest deviation between the measured and simulated evaporation occurred in a late phase of the growing season with a yellow non-transpiring canopy and, after harvesting, with stubble. The simulated surface temperature was mainly within 2 K of direct measurements, both in bare soil and dense canopy situations. The study showed that the scheme is applicable for practical use, since the weather input parameters required are limited to those which are available as normal synoptic observations. # 1998 Elsevier Science B.V. All rights reserved. Keywords: Evapotranspiration; Modelling; Crop; Measurements
1. Introduction The estimation of total evaporation and its components using easily-measurable meteorological variables is of great importance e.g. in crop growth monitoring programs, or in many practical operations, such as irrigation scheduling for farmers. For applications where the vegetation can be treated as a single layer *Corresponding author. Tel.: 00358 919291; fax: 00358 919294103; e-mail: [email protected] 0168-1923/98/$19.00 # 1998 Elsevier Science B.V. All rights reserved. PII S0168-1923(98)00065-3
(`big leaf'), the Penman±Monteith (P±M) combination equation has proven useful; this is the case when the crop canopy is well-developed and its cover is closed (Monteith, 1965). Over the entire growing season, however, this approach faces complications due to the signi®cant seasonal changes of the vegetation cover, as well as the varying tillage of the soil. Recent theoretical development of the P±M concept has led to the compartment schemes in which soil surface evaporation and transpiration from the canopy are resolved separately (Shuttleworth and Wallace,
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1985, Choudhury and Monteith, 1988, Noilhan and Planton, 1989 and Kustas, 1990). The Shuttleworth±Wallace (S±W) scheme has been validated with ®eld measurements by several authors for different types of sites and canopies. LaFleur's and Rouse's (1990) site was a subarctic wetland sedge meadow: they found excellent agreement between the measured and calculated evaporation. The soil surface below the canopy was wet all the time, causing the soil evaporation to take place at the potential rate. The S±W scheme was used for arid conditions by Nichols (1992), who evaluated the scheme on semiarid rangeland, where the vegetation consisted of sparse shrubs without any vegetation sublayer. Nichols used the approach of Shuttleworth and Gurney (1990) in the determination of the mean canopy resistance, needing sophisticated measurements of canopy foliage and soil surface temperatures. The estimate of transpiration was reasonably good, but the result for the soil surface evaporation was less satisfactory, although it played a minor role in the total ¯ux, due to the very dry soil surface. Iritz et al. (1997) used the S±W scheme, in the same form as was used in this paper, for a cultivated willow stand. From these studies, one may conclude that the S±W type of approach is most useful in the assessment of evapotranspiration from vegetated surfaces. In our approach the object of interest was a barley ®eld; the period of investigation was extended over the whole growing season, ranging from pre-sowing, through the various phenological phases of the annual crop, up to post-harvesting. This provided a wide range of canopy densities, with a leaf area index varying between zero and four. The factors driving the energy ¯uxes varied between rainy and dry periods, leading to a signi®cant variation of the soil moisture within the rooting depth of the crop. The control of transpiration by soil moisture and soil surface evaporation was therefore considered as an equally important part of the scheme. Another aim was to develop the scheme in such a way that the water balance was included. The S±W scheme was tested against measurements of evapotranspiration made with the Bowen-ratio method over two summers at an agricultural site in southern Finland. The overall goal was to identify the number of necessary input parameters to the scheme, while still allowing its use in practical applications.
2. The model 2.1. Overview of the Shuttleworth±Wallace scheme The S±W scheme is one-dimensional and describes the energy partition of a sparse canopy. The basic assumption is that the water vapour ¯ux from the soil to the atmosphere can take place simultaneously from the soil surface as soil evaporation, through plants as transpiration and thirdly as evaporation of the intercepted water. Practically, the scheme consists of a mathematical formulation of the resistances that control the vapour ¯ow. The procedure used in this study is based on the work of Shuttleworth and Wallace (1985) and is not repeated here in so far as the equations are identical. The procedure is extended in terms of the soil surface and bulk canopy resistances, as well as in the calculation of the aerodynamic resistances. 2.2. Calculation of aerodynamic resistances The aerodynamic resistance, raa , for stable and unstable conditions was calculated with an analytical method suggested by Choudhury et al. (1986). The required input variables are the aerodynamic surface temperature, Ts, which is de®ned to prevail at the virtual source/sink level of sensible heat, the reference height temperature, Tz and the wind speed at the reference height, u. In our case the reference height z was 2 m above the soil surface. The stability functions for momentum and sensible heat M and H were considered to be equal and expressed as:
B ÿ B2 ÿ 4aC0:5 = 2a
(1)
where: a1
(2)
B ln z ÿ d=z0H 2 ln z ÿ d=z0M
(3)
C lnf z ÿ d=z0M g2
(4)
5 z ÿ dg T0 ÿ
Tz = Tz u2z
(5)
and as a ®nal result the resistance is given for unstable conditions by: zÿd zÿd a ÿ ln ÿ k2 u ra ln z0M z0H (6)
T. Tourula, M. Heikinheimo / Agricultural and Forest Meteorology 91 (1998) 237±250
where k is the von Karman constant. For stable conditions the resistance is given by: zÿd zÿd a ln k2 u 1 0:75 (7) ra ln z0M z0H The displacement height d and roughness lengths for momentum ¯ux, zM, sensible heat ¯ux, zH and latent heat ¯ux, zE, depend in the method of Choudhury et al. (1986) on the canopy height h as follows (Legg and Long, 1975 and Garratt, 1978) d 0:56h
(8)
zM 0:3 h ÿ d
(9)
zH zE zM =7
(10)
The aerodynamic surface temperature, Ts, was calculated with a method given by Lhomme (1992). This method requires the bulk surface resistance rsurf as an input parameter, which can be calculated from the canopy and soil surface resistances rsc and rss as follows: rsurf 1= 1=rsc 1=rss
(11)
The aerodynamic surface temperature, Ts, can be calculated by: Ts Tz !=cp Rn ÿ G ÿ != Dz = raa rsurf (12) where Dz is the vapour pressure de®cit of the air at the reference level z. ! is de®ned by: ! 1=1=r0
1=raa
= raa
rsurf
(13)
where r0 is: r0 cp =4"Tz3
(14)
and is the slope of the saturated vapour pressure curve determined at the temperature of the air Tz, " the emissivity of the surface (0.98) and the Stefan± Boltzmann constant. Because the aerodynamic resistance raa was needed for the calculation of the aerodynamic surface temperature, the calculation was iterated a few times to obtain the adjustment of raa and Ts to the prevailing stability conditions. Normally, the ®nal values for Ts and raa converged within two or three loops to a precision of one per cent. The initial values of the resistances were obtained using a direct method given by Shuttleworth and Wallace (1985). Furthermore,
239
because rsurf depends directly on the aerodynamic surface temperature and on the vapour pressure de®cit of the canopy air via the aerodynamic and canopy resistances, the whole scheme was iterated ®ve times at each time step. The aerodynamic resistance within the canopy, ras , was calculated, as in S±W, using the (K-) theory of an eddy diffusivity assumed to vary exponentially with height within the canopy. Similarity between momentum, sensible heat and vapour transfer, as well as neutral strati®cation, were assumed. The value of ras was leaf-area-dependent, as given in the S±W scheme. It varied linearly between the asymptotic limits of a bare soil situation and a full canopy cover. The magnitude of rac , which controls transfer between the surface of the vegetation and the canopy air, was considered to be small compared to other resistances and a constant value of 5 s/m was used (Smith et al., 1988). Compared to the original S±W scheme, the main difference was that the stability effect was included in raa . On the other hand, no leaf area dependency is taken into account when calculating raa as was made in the original S±W scheme. This simpli®cation should play only a minor numerical role because, according to the sensitivity analysis of Shuttleworth and Wallace (1985), extreme changes in the original parameterization of raa and ras have less than a 5% effect on the total evaporation rate. 2.3. Calculation of canopy resistance To get an independent estimate of the canopy resistance, rM, the original Penman±Monteith equation was inverted (Eq. (15)) and solved for the surface resistance. A two-week test period (starting 1 July 1991) was selected for which the crop canopy was fully-developed (leaf area index>3) and closed. Under such conditions the evaporation from the soil through the canopy was assumed to be small and hence the calculated surface resistance closely approximated the canopy resistance rsc . raa Rn ÿ G cp es ÿ e0 =raa rM ÿ
Etot (15) where cp is the heat capacity of air, es the saturated and e0 the ambient vapour pressure at a reference
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height, the psychometric constant, Rn the net radiation and G the soil heat ¯ux. To determine the value of the minimum canopy resistance, rsmin , 5 cases, lasting a few hours on separate days during the two week test period, were found having minimum limitations by the environment. The soil moisture was near ®eld capacity, the temperature was between 178C and 258C, the vapour pressure de®cit at the 2 m level was below 5 hPa and the global radiation was over 400 W mÿ2. It was assumed that the stomata were fully open during these optimal conditions and that the surface resistance rsc , calculated from (Eq. (15)), represented its minimum value rsmin . To correct the value for the effect of the shading of leaves deeper in the canopy, rsmin was divided by a constant A, which was calculated by the method based on Noilhan and Planton (1989). A
1f f rsmin =rsmax
(16)
where: f 0:55Rn =L
(17)
where L is the leaf area index of green and yellow leaves. For the barley crop, we obtained an average value of 90 s/m with a variation of 40 s/m. Previously, KoÈrner et al. (1979) has reported corresponding values ranging from 90 to 100 s/m. It is emphasised that these values are not bulk values for the whole canopy but are mean values per unit area of Green Area Index, LG (1 m2). The canopy resistance was parameterized according to the method given by Avissar et al. (1985) as a multiplicative response to several environmental factors expressed as F1 ; . . . ; F4 . rsc rsmin = F1 F2 F3 F4 LG
(18)
where rsmin represents the minimum resistance with fully open stomata and LG is the total green area contributing to transpiration. The use of LG allows the use of this parameterization throughout the whole growing season, because only the transpirating partition of the leaves is taken into account. The functions F1 ; . . . ; F4 in (Eq. (18)) refer to the in¯uence of global radiation (F1), leaf temperature (F2), within-canopy vapour pressure de®cit (F3) and plant-available soil moisture content (F4), respec-
tively. All F-functions have the same general form: Fi 1=f1 expÿS Xi ÿ bg
(19)
where the subscript i refers to the environmental factors, whose values are given by Xi. S and b are species-speci®c constants. The values of the F-functions can vary between 0 and 1, with 0 indicating full closure of the stomata and 1 fully-open stomata. In the case where one or more of the F-functions reach zero, the value of (Eq. (18)) becomes unde®ned and rsc is given a maximum value of 50 000 s/m. This corresponds to the molecular diffusivity of water vapour transfer through leaf cuticula. Due to the lack of global radiation measurements, we used twice the value of the net radiation as an estimate for it. This should not much affect the result, because during daytime the amount of radiation was not a limiting factor. The role of radiation was mainly to act like a switch, which turned off the evaporation during the night time. The leaf temperature was assumed to be identical to the aerodynamic surface temperature Ts, which was calculated by (Eq. (12)). The vapour pressure de®cit of the canopy air, D0, was obtained as in the original S±W scheme. The method was calibrated against the measured evapotranspiration in a two-week period (starting 1 July 1991). The parameters S and b given in Table 1 were adjusted, keeping in mind that they should differ as little as possible from the physical values determined by the measurements for similar species (Kueppers, 1988 and Turner, 1991). The parameter set was a compromise between the optimal mathematical solution and physically reasonable values. When varying the parameters around their given values, any signi®cant improvement in the modelled transpiration on a daily basis was not found. Table 1 Parameters used in the Avissar scheme for the bulk canopy resistance Parameter Global rad. Leaf temperature Vapour pressure deficit Soil moisture
Units ÿ2
Wm K Pa Vol.%
S
b
0.03 0.41 ÿ0.003 3000
40 280 700 25
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2.4. Calculation of the soil surface resistance The resistance to moisture transfer from the soil, rss , was calculated using a hypothetical two-layer parameterization proposed by Choudhury and Monteith (1988). The upper hypothetical dry layer l1 increases in depth as the soil evaporation Esoil takes place and decreases as it rains, P, in accordance with Eq. (20). 2 is the volumetric soil moisture of the lower layer, l2, reaching down to the rooting depth. @l1 Esoil ÿ P=2 @t
(20)
The lower soil layer, l2, is moist. The evaporation from the soil is assumed to originate from the top of that layer. The soil surface resistance, rss is kept at zero until l1 reaches 0.2 mm. After that threshold, rss increases in proportion to l1 according to the following relation: rss
ÿ5
1:41 10 l1
(21)
The total volumetric moisture content, tot, from the soil surface down to depth l2 is used for the calculation of the canopy resistance. This value differs by just a few percent from 2, which is the volumetric moisture of the lower layer only and was calculated with a simple bucket method. The soil moisture 2 is only reduced by uptake by the plant roots i.e. transpiration, Etrans and increases by supply from in®ltrated rain water, Pinf. @2 1 Pinf ÿ Etrans @t w l 2
(22)
where t is time and w is the density of water. The upwelling of moisture from ground water is assumed to be negligible, due to the clay soil composition and the presence of underground drainage channels. During rain, droplets ®rst fall on the leaves and the interception storage is ®lled. The remaining water is then used to wet the 0.2 mm deep buffer at the soil surface, after which the upper dry layer l1 starts to ®ll, but only up to moisture 2. Filling the upper layer is performed according to Eq. (20) i.e. the depth of the layer decreases. Upon ®lling, i.e. the vanishing of l1, the whole soil layer from the surface to depth l2 attains the original moisture 2. If the rain still continues, 2 increases according to Eq. (22) up to ®eld capacity, after which runoff takes place.
241
2.5. Calculation of the evaporation of intercepted water The evaporation of the intercepted water, Eint, was calculated by the method suggested by Noilhan and Planton (1989) cp Wfr es ÿ e0 =raa (23) Eint
where Wfr is a power function of the moisture content of the interception reservoir, calculated as proposed by Deardorff (1978): Wr 2=3 (24) Wfr Wrmax where Wr is the actual amount of intercepted water and Wrmax is the maximal possible amount de®ned by Dickinson (1984): Wrmax 0:2L
(25)
where L is the leaf area index of green and yellow leaves. 3. Measurements Measurements were carried out on a non-irrigated barley ®eld (Hordeum vulgare) in Southern Finland (608250 N latitude, 248240 E, longitude, 47 m altitude). The soil texture was sandy clay and the ®eld sloped gently to the north-east. The ®eld contained underground drainage channels at a depth of about 1 m. The fetch of open homogeneous ®eld from the surrounding coniferous forest boundary was 300±1000 m depending on the wind direction. For this study we used data sets from the summers of 1991 and 1992. In 1991 the 125-day period began on 20 May and ended on 31 August. In 1992 the ®rst day of the measurements was 20 May and the last 18 August. These two summers differed signi®cantly in terms of precipitation. Summer 1991 was more or less normal with alternating dry and rainy periods and a well-developed crop canopy. Mean temperature and wind speed were close to normal long-term values. The ®rst half of summer 1992 was extremely dry, with the consequence that severe drought hindered the development of the crop canopy. The leaf area index reached a value of 1, being about 50% smaller than in
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Fig. 1. Seasonal variation of green leaf area index (LLG), total green area index (LG) and canopy height (hc) in 1991 and 1992.
1991. In July and August the weather was normal with rainy periods. Evapotranspiration, Emeas, was estimated by the Bowen-ratio method (the instrumental set-up was that commercially available from Campbell Science, UK), using a 20 min averaging period. The distance between the lower and the upper vapour pressure and temperature measurement levels was 1 m. The lower level was kept at approximately 1 m above the soil/top of the canopy. Net radiation was measured with a Fritschen-type (Q5, Campbell Science, UK) domed radiometer. In addition, air temperature, relative humidity and wind speed were measured at a ®xed 2.2 m level above the soil surface. Occurrences of rain or dew were monitored with a wetness sensor (Model 237, Campbell Science). For certain periods, the radiative skin temperature of the foliage was measured with an instrument manufactured by Everest Interscience (model 4000, angle of view 158). The instrument was placed at a height of 2.5 m and was pointed eastward, tilted 208 below the horizon. An internal checking routine was developed to evaluate the measured variables and to clearly mark erroneous values. Periods of bad data were excluded
from the summing of the daily totals. Daily totals of ¯ux quantities were calculated for the whole 24 h period. Daily means of other quantities, i.e. canopy and soil resistances, were calculated for the daytime, between 09±18 h local time. Daily precipitation was obtained partly from a nearby climatological station located 2 km east of the site. The daily amounts of precipitation were split into 20 min values based on the information from the wetness sensor and assuming a constant rainfall intensity. Temporarily, the precipitation was measured at the site using a tipping-bucket-type rain gauge. Such periods were from 1 July to 15 August in 1991 and from 27 May to 3 July in 1992. When this data was available, it was used in the calculations. In 1992 the soil moisture was measured about once a week with a neutron probe at one point in the ®eld close to the other instruments. An estimate of the crop's phytometric properties was obtained by the periodic destructive sampling throughout the life cycle of the crop. The measured quantities were: leaf area index, L, of green and yellow leaves, leaf area index of green leaves only, LLG, stem green area index, LSG and height of canopy, hc. The
T. Tourula, M. Heikinheimo / Agricultural and Forest Meteorology 91 (1998) 237±250
total green area index, LG, was de®ned as follows: LG LLG 0:5LSG
(26)
The factor 0.5 takes into account the fact that on the surface of stems the density of stomatal pores is sparser than on leaves. All areas were expressed per unit ground area, Fig. 1 and the curves presented are ®tted to measured points. The development of plant roots was estimated assuming a sowing depth of 5 cm and using the root growing rates and rooting depths measured by Ilola et al. (1988) for a similar soil type and climate conditions. The maximum rooting depth was set somewhat arbitrarily at 50 cm in 1991 and at 25 cm in 1992. 4. Results 4.1. Surface temperature as the scheme output The surface temperature is a key parameter for the aerodynamic resistance, because it largely determines the stability of the surface layer. In dense canopies, foliage surface temperature serves as a ®rst order estimate of the temperature of the transpiring leaves, which controls transpiration through the canopy resistance. For interpreting the modelled results it was important to estimate how well the calculated aerodynamic surface temperature, Ts, agreed with the measured one, Tsm. Two weeks were selected for evaluation. During the week starting 18 May 1992 the soil was completely bare and freshly tilled due to sowing carried out just a few days before (Fig. 2(a)). During the week starting 1 July 1991 the barley canopy was fully developed with an LG>3 (Fig. 2(b)). The ®rst day of the week starting 18 May 1992 was mainly sunny, with a relatively high surface temperature. Around mid-day the calculated temperature was about 58 lower than that measured. One probable reason for this was the orientation of the IR-sensor towards the east, thus causing the warmer side of the soil granules to face the sensor. The estimation of the soil heat ¯ux could also have been unrepresentative due to the strong moisture gradient at the surface and the large horizontal variability of moisture and other soil properties. Over the following ®ve, mostly cloudy, days the deviation was smaller, within the limits
243
of 28. The last day was again partly sunny with somewhat larger deviations. In conclusion, it can be stated that in bare soil conditions the model is able to handle cloudy days better than sunny days with an extremely high surface temperature compared to the air temperature. The assumption of the same roughness length of heat to momentum ratio (zH/zM) for bare soil as for a dense canopy may partly explain the deviation. The period before the week starting 1 July 1991 was rainy. The ®rst three days of the week starting 1 July 1991 were cloudy, with a little rain occurring on the ®rst and third days. The last four days were mainly sunny and warm. The overall agreement during the week was good, considering the large daily variability of actual and calculated temperatures. Though the diurnal amplitude of the calculated temperature tended to be smaller, the deviation remained mainly within 28. A small time shift was also seen, i.e. during the mornings the calculated temperature rose slightly earlier and in the evenings fell somewhat earlier. One possible cause for the deviation in a dense canopy situation could be that the calculated value represented the source level of the sensible heat ¯ux rather than the top of the canopy seen by the IR-sensor (Choudhury et al., 1986). Despite the temporal discrepancies between the measured and calculated surface temperatures the overall correspondence was good giving con®dence to the calculation of the aerodynamic resistance and canopy resistance. Similar conclusions have been reported e.g. by Smith et al. (1988). 4.2. The behaviour of the vapour pressure deficit within the canopy The vapour pressure de®cit within the canopy, D0, is an important parameter, because it controls transpiration through its in¯uence on stomatal resistance. Two contrasting periods were selected to assess the magnitude of this effect. On the week starting 8 June 1991 the canopy was very sparse, with an LG of about 0.4 (Fig. 3(a)). The behaviour of D0 showed features similar to what one would expect for bare soil conditions, where the solar radiation strongly heats the soil surface, causing a large difference between the temperatures at the reference and the canopy/soil levels. The temperature difference is clearly illustrated
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Fig. 2. Comparison of the calculated surface temperature (Ts), measured surface temperature (Tsm) and measured air temperature (Tz), (a) for bare soil conditions during the week beginning 18 May 1992; (b) for closed canopy conditions during the week beginning 1 July 1991.
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Fig. 3. Simulated canopy level vapour pressure deficit (D0) compared to measured reference level vapour pressure deficit (Dz), (a) for sparse canopy conditions during the week beginning 8 June 1991; (b) for closed canopy conditions during the week beginning 1 July 1991.
in Fig. 2(a). The in¯uence of D0 on the calculated evapotranspiration is negligible, due to the minor role of transpiration in this situation.
During the week starting 1 July 1991, with a dense canopy, the values of D0 were smaller and close to the vapour pressure de®cit at the reference level, Dz
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(Fig. 3(b). D0 increased during the morning hours above Dz, but decreased below Dz in the afternoon, when transpiration moistened the canopy air. It is to be pointed out that D0 and the bulk canopy resistance are not independent variables. There is strong positive feedback: when the canopy resistance decreases, transpiration increases, leading to a decreasing D0, which in turn causes a further decrease in the canopy resistance.
By studying some sub-periods of the simulation, some noteworthy points can be discovered. It can clearly be seen that the magnitude of the soil evaporation is highly dependent on the canopy density. With a dense canopy at the beginning of July 1991, the soil evaporation did not exceed 15% of the total ¯ux, even in the case of a wet soil surface. At the end of June 1992, with a sparse canopy and wet soil surface conditions, the proportion of the soil evaporation reached a maximum of 28%. The day-to-day variability of evapotranspiration was large, but it was well-simulated for most of the time. This indicates that the mechanisms regulating transpiration were rather well covered by the present parameterization. At the beginning of summer 1992, Bowen-ratio measurements were started immediately after cultivation and sowing, when the soil was still completely bare. This provided the possibility of verifying the calculated soil surface evaporation against measurements. The daily evaporation amounts were low due to the dry spell (Fig. 4(a)). During the dry period the soil surface resistance continuously increased, but daily evaporation was still rather well simulated. The evaporation of the intercepted rain water was also included in Fig. 4. It improved the result in most cases, but in some cases it made them poorer, however. When L was large, the in¯uence was clearly positive, as seen on e.g. 29 June 1991. Later, in August, the interception part improved the result during some periods, when the canopy was yellow and hence the
4.3. Simulations of the total evapotranspiration The simulations of total evapotranspiration were made for two full growing cycles of barley in 1991 and 1992. The seasons differed from each other, which is indicated for example by the maximum LG (see Fig. 1), resulting in a signi®cant difference in the levels of the evapotranspiration (see Fig. 4). The seasonal sum of the total evapotranspiration Etot (the sum of soil surface evaporation, Esoil, transpiration, Etrans and evaporation of intercepted water, Eint) differed signi®cantly from summer 1991 to summer 1992, being in reasonable agreement with the measured evapotranspiration in both years (Table 2 and Fig. 4), indicating that the separate terms of the simulated evapotranspiration were of realistic magnitude. Signi®cant discrepancies arose under conditions of mature crop and stubble in August and September 1991, as illustrated in Table 2(a).
Table 2 Cumulative precipitation and evaporation for selected sub-periods in (a) 1991 and (b) 1992 (a) 1991 P Eint Esoil Etrans Etot Emeas
[mm] [mm] [mm] [mm] [mm] [mm]
20±31 May 9 0 7 0 7 ±
1±30 June
1±31 July
1±31 August
70 6 22 22 50 ±
18 5 12 60 77 80
181 10 21 3 34 50 1±18 August
(b) 1992
18±31 May
1±30 June
1±31 July
P Eint Esoil
0 0 7 1 8 10
11 2 9 30 41 39
30 6 16 19 41 39
trans
Etot Emeas
[mm] [mm] [mm] [mm] [mm] [mm]
51 2 15 1 18 17
1±21 September 23 4 9 0 13 27 18 May±18 Aug. 92 10 47 51 108 105
20 May± 21 September
1 July± 21 September
301 25 71 85 181 ±
222 19 42 63 124 157
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Fig. 4. Comparison of the calculated daily total evapotranspiration (upper thin line) to the measured values (thick line) obtained by Bowenratio method for the growing seasons in 1991 (a) and 1992 (b). The shaded areas correspond to the estimated components of total evapotranspiration: transpiration (Etrans), soil evaporation (Esoil) and evaporation of intercepted rainfall (Eint).
transpiration was small. On a hourly basis the function of the interception part varied due to the unrepresentative precipitation measurement. This is illustrated in
Fig. 4 on some isolated days where the simulated result clearly exceeded the measured value. The evaporation of intercepted water in accumulated amounts
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as a fraction of the total evapotranspiration in 1991 was 14% while it was 9% in 1992, emphasising the importance of this part. The evaporation of intercepted water could exceed about 50% of the total budget of the total daily evapotranspiration, especially on rainy days of a shower type. There were two sub-periods during summer 1991 in which a relatively large discrepancy between the calculated and measured evaporation occurred. The ®rst was when the crop had reached its maturity and the green part of the canopy was decreasing rapidly. During this period the estimation of the LG (Green Area Index), i.e. the area of the transpiring surface of the canopy, was very dif®cult. The second period of discrepancy was found after harvesting, i.e. when the ®eld was covered with 15 cm tall stubble and straw, whose characteristics were dif®cult to parameterize. The albedo, the isolation of the soil surface by the surface residue and interception are all factors which may have caused possible inaccuracy in the result. One aim was to introduce soil moisture into the scheme. The method was in essence simple, but realistic. The curves of volumetric soil moisture calculated for the soil layer from the surface to the rooting depth are plotted in Fig. 5 . Unfortunately the corresponding weekly measurements were only available for 1992. In 1991, the initial pro®le of soil moisture was set at ®eld capacity, because after the melting of the snow there was enough water available. In 1992, measurements provided the initial value for the soil moisture. It is to be noted that the soil moisture measurements were only made at one point and were probably not fully representative of the whole ®eld. This may partly explain the differences between the measured and modelled moistures. However, the overall agreement was good and the shape of the modelled moisture followed the trend of the measured points nicely. This gives con®dence in the simple approach used here, in which the soil moisture budget does not contain in®ltration to ground water or percolation. The daily precipitation is also shown as columns and the signi®cant difference between the two seasons is clearly seen. The soil surface resistance, rss , rapidly increased as the soil dried. When precipitation reached the soil surface so as to wet it, rss dropped to zero. However, since small amounts of water intercepted at the soil surface are soon evapo-
rated back into the air, rss rose rapidly to close to its previous level. 5. Conclusions By using a simple two-layer scheme for evapotranspiration, it was possible to estimate the actual total evaporation with an accuracy that is considered suf®cient for practical applications. The water balance of a crop ®eld, at least in the case of a simple uniform soil texture, could be estimated using a simple bucket-type two-layer soil parameterization. This kind of resistance network parameterization allows one to study the sub-processes of water transport from the soil to the atmosphere separately. One of the important factors controlling the ¯ux was found to be the surface temperature, affecting both the aerodynamic and canopy resistance. The vapour pressure de®cit of the canopy layer was also important, controlling the evaporation demand and canopy resistance. In our approach the calculation scheme was kept as general as possible, allowing easy adaptability to different kind of sites with varying vegetation and soil properties. The aerodynamic resistance does not need sophisticated measured parameters, such as the canopy surface temperature or wind pro®le. Nevertheless the canopy resistance, another signi®cant term in the water transport of vegetated sites, is easy to adjust for different vegetation, since the parameterization includes four separate factors. The input variables required were restricted to those which are available directly or are able to be calculated from synoptic observations. Temperature, humidity and wind speed are directly available. A dif®cult variable to handle in this respect is the precipitation, for which at least hourly values are required. Some algorithms do exist to create hourly precipitation data from measurements made every 12 h (Lystad and Tallaksen, 1991). The available energy (RnÿG) is a variable which is not measured at normal synoptic stations. There are methods by which it is possible to estimate global radiation using observations of cloudiness and net radiation (VenaÈlaÈinen and Heikinheimo, 1996). Taking all the previous points into account, it would be possible to use the scheme based purely on synoptic data, without any sophisticated micrometeorological measurements.
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Fig. 5. Comparison of the daily means of the measured and modelled soild moisture of the rooting layer (meas and tot) shown with the corresponding soil surface resistance (rss ) and precipitation (P) for (a) 1991 and (b) 1992.
This opens a broad perspective for practical applications, such as the real-time monitoring of soil moisture for large agricultural areas e.g. for purposes of irriga-
tion scheduling, or the monitoring of forest evapotranspiration for hydrological applications. For these kinds of large-scale simulation the canopy properties
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