- Email: [email protected]
Leaf wetness duration in a field bean canopy
Agricultural and Forest Meteorology, 51 (1990) 281-292
281
Elsevier Science Publishers B.V., A m s t e r d a m - - Printed in The Netherlands
Leaf wetness duration in a field bean canopy L. Huber and B. Itier Institut National de la Recherche Agronomique, Centre de Recherches de Grignon-Massy-Paris, Station de Bioclimatologie, F - 78850 Thiverval-Grignon (France} (Received July 8, 1989; revision accepted January 4, 1990)
ABSTRACT Huber, L. and Itier, B., 1990. Leaf wetness duration in a field bean canopy. Agric. For. Meteoroi., 51: 281-292. The experimental testing of a multi-layer model to simulate surface wetness duration (SWD) in a canopy is presented. A previous model was modified by includingthe heat conduction from dry areas of leaves to water deposits. Field tests after sprinkling during humid and cloudy weather are reported for 10 days in the summers of 1985 and 1986. The discussion is focused on the importance of heat conduction and the influence of water distribution on leaves in determining SWD.
INTRODUCTION
Surface wetness duration (SWD) is an important factor in agriculture, not only for cultural practices such as harvesting or hay drying but also for the biological cycles of pests (Van der Wal, 1978 ). In disease predictive schemes, the influence of SWD on infection phases is commonly determined under controlled conditions (Rotem, 1988 ). To obtain an estimate of SWD in the field, several methods have been investigated: either a calculation using local relationships between SWD and meteorological variables (Crowe et al., 1978; Gillespie and Sutton, 1979) or using direct measurements of SWD by means of appropriate sensors (Gillespie and Kidd, 1978; H~ickel, 1980, 1984; Weiss and Hagen, 1983; Gillespie and Duan, 1987 ). Jones ( 1986 ) and Sutton et al. ( 1988 ) reviewed different types of sensors. Measured values of SWD are highly dependent on the type of sensor used (Weiss and Hagen, 1983; Huband and Butler, 1984 ). Furthermore, a good description of SWD in the field would need a large number of sensors to account for the high variability (Huber and Wehrlen, 1988 ). Hence, attempts have been made to build deterministic models in order to simulate SWD using standard weather station data or micrometeorological data. Beside simple models devoted to SWD estimates of particular organs or canopy positions (Monteith and Butler, 1979; Pedro and Gillespie, 1982; 0168-1923/90/$03.50
© 1990 Elsevier Science Publishers B.V.
282
L. HUBER AND B. ITIER
Payen, 1983), multi-layer models have been proposed to simulate the leaf wetness duration profile within the canopy in cases of rain or dew (Goudriaan, 1977; Norman, 1979; Thompson, 1981; Butler, 1986). None of these approaches, excepted Butler's model, include heat conduction from the dry parts to the wetted parts of leaves. Only two models have been tested under field conditions: Weiss and Norman (1987) have presented field tests of the CUPID model (Norman, 1979) under dew conditions for 5 days; Butler (1986) has only presented a l-day comparison in the case of wetness due to rain. The aim of this paper is to present the experimental tests under field conditions of a multi-layer model, including heat conduction, to simulate the SWD profile after a rain event using a set of data obtained during 10 days. METHODS
Model The SWD profile was simulated using a steady state one-dimensional multilayer model. A previous model (Huber, 1988) was modified to take into account the heat conduction from dry areas to water deposits on leaves of a partially wet canopy. External variables are air temperature, dew-point, wind velocity and net radiation measured at a reference height, i.e. 2 m above the top of the canopy. The plant canopy is assumed to be horizontally uniform and its structure is described by means of a leaf area density profile, the mean height of the plants and a characteristic dimension of leaves. The windspeed profile u (z) within the crop is simulated using an analytical expression as proposed by Landsberg and James ( 1971 ):
u(z)=u(h) [ l + a ( 1 - z / h ) ] - 2 where a = 1.3, h is the height of the canopy and z the height above the soil. The turbulent exchanges in the air are described using K-theory. The turbulent diffusivity profile K(z) above and within the canopy varies as proposed by Thorn ( 1971 ) for field beans:
:K(z)=ku* ( z - d ) where d=0.75 h for h/3
for z > h
k is the yon Karman's constant (0.4), u , the friction velocity and d is the height of the zero plane displacement. Owing to low net radiation levels and low values of Bowen ratio, the aerodynamic resistance Ra above the canopy is computed using a forced convection formula:
283
LEAF W E T N E S S D U R A T I O N IN F I E L D BEAN C A N O P Y
Ra= (k u , ) - ' Ln[ ( z ~ f - d ) / ( h - d ) ] where Zref is the reference height above the canopy where the forcing variables are measured. For the same reason, exchange coefficients of both wet and dry parts of leaves are computed as a function of their Nusselt number (Nu). The characteristic dimension used for computing Nu corresponds to the mean width of leaves. The Nusselt number is computed as proposed by Finnigan and Raupach ( 19 8 7 ) using Reynolds (Re) and Prandtl (Pr = 0.7 ) numbers: N u = 1.3 Re I/2 Pr ~/3 To govern the evapotranspiration process on so-called dry parts of leaf surfaces, the stomatal resistance profile Rs(z) was determined using the global radiation profile Rg ( z ) (Avissar et al., 19 8 5 ):
ifO
Rs(z)-l-Rsmlax --1
RS m i n
--1
--
Rs m a x
--
Rg(z)-Rginf Rgsup- Rginf
if Rgsup< Rg(z) then Rs(z) =RSmin Shown in these equations are the minimal and maximal stomatal resistances (RSmin and Rsmax) corresponding respectively to two thresholds of global radiation (Rgsup and Rginf). The soil-plant system is divided in n - 1 horizontal layers and a soil layer. Every layer of the canopy is divided into two sublayers: a wetted sublayer and a dry sublayer. Only the upward leaf surface may be wetted during a rainy event (it would be different in the case of dew because of condensation upon both leaf surfaces). The energy balance equation for each sublayer j ( j = 1: wet sublayer; j = 2: dry sublayer) of a canopy layer i ( 1 < i < n - 1 ) is given by:
W(i,j) ~Rn(i) =~H(i,j) +#LE(i,j) +#C(i,j) where W(i,j) is the absorbed fraction of available energy ~Rn (i) by sublayer j in layer i, and ~H(i,j) and ~LE(i,j) are respectively the sensible heat flux and latent heat flux densities emanating for both sublayers. ~C(i,j) is the heat conduction flux density (from the dry parts to the water deposits for j = 2 and inversely for j = 1 ). ~H(i,j), ~LE(i,j) and ~C(i,j) are given by the following expressions:
284
L. HUBER AND B. ITIER
OH( i,j) =p Cp hh( i,j) [ Ts( i , j ) - Ta( i) ] OLE( i,j) =? Cp hv( i,j) {es[ Ts( i,j) ] -ea( i) }/v OC( i,j) = 0 ( j ) k( i) [ Ts( i,2 ) - Ts( i, 1 ) ] where 0(j) = + 1 if j = 1 and 0(j) = - 1 if j = 2 and k( i) =2 ~z1/2 q [ W( i) LAI(i) Nw( i) Nl( i) ]1/2 Symbols in these equations are the air density (p), specific heat of air at constant pressure (Cp), psychrometric constant (~), saturated vapor density function (es(T) ) and the heat conduction coefficient (q). Ts(i,j) is the surface temperature of the sublayer j in the layer i, Ta (i) and ea (i) are the air temperature and the vapor pressure in the layer i; hh(i,j) and hv(i,j) are the exchange coefficients for heat and vapor transfer respectively and are expressed as functions of the computed Nu, stomatal resistance and wetted area percentage of each layer. LAI (i) corresponds to the fraction of LAI in the layer i and W(i) is defined as the wetted area percentage ( W ( i ) = 1 if the leaves of the layer i are completely wet on the upper side). Nw(i) is the number of individual wet surfaces per leaf, Nl(i) is the number of leaves in the layer i. The expression for the coefficient k (i) is obtained by assuming that the conduction flux is proportional to the total circumference of the individual wet surfaces in the layer i, as proposed by Butler ( 1985 ) who obtained an estimate of the effective thermal conductivity coefficient in the case of heat conduction to an isolated drop of water on a wheat leaf. For sensitivity analysis purposes, q was allowed to vary from 0 to 0.25 W m-1 K-1. The mean value obtained by Butler on winter wheat leaves is equal to 0.11 W m - 1 K- 1. For the soil layer n there is only one energy balance equation:
ORn ( n ) = 0 H ( n ) + OLE ( n ) To take into account the soil contributions OH(n) and OLE(n) to sensible heat flux and latent heat flux densities, we assume exchange coefficients hh (n) and hv (n) as proposed by Goudriaan ( 1977 ) and a surface resistance as proposed by Shuttleworth and Wallace ( 1985 ). The available net radiation ORn (i) in layer i is computed using Impens and Lemeur ( 1969): if 1 < i < n - 1: ORn(i)=Rn(h) { e x p [ - K F ( i - l ) ] - e x p [ - K F ( i ) ] } if i = n: ORn(n) =Rn(h) exp[ - K F ( n - 1 ) ] - G where K is the extinction coefficient ( K = 0 . 5 for overcast days), F(i) the cumulative leaf area density function from the top of the canopy to the bottom of layer i and G is the conduction heat flux into the ground estimated as 20% of the net radiation available in the layer n - 1. The partitioning of the
LEAF WETNESS DURATION IN FIELD BEAN CANOPY
285
available net radiation ~Rn (i) in a given canopy layer between both wet and dry sublayers linearly depends on wetted area percentage W(i) in the layer involved:
W( i,1 ) = W( i) /2 and W(i,2) = l - W( i) /2 Initial conditions required for the model are the surface water storage of the canopy (S) and the initial value Wo (i) of the wet area percentage ( W ( i ) ) in each layer i. The initial value of W(i) is assumed to be the same (Wo) in each layer i. The time evolutions of the wet area percentage W(i) and the water amount on the leaves Q (i) in each layer i are computed at the end of every time step by means of (Huber, 1988 ):
W( i) / Wo= [Q( i) / Qo( i) ]P where: Qo( i) = Wo( i) (S/LAI) LAI(i) The exponent fl depends on surface water distribution (fl=0 for water films with constant wetted area, fl= 2/3 for hemispheric shaped drops). Following Butler's ( 1985 ) laboratory experiments the coefficient (r/) for heat transfer by conduction from wet to dry parts of leaves was kept constant throughout the wetness duration and independent of changes in the size of wet areas. The numerical procedure uses both Chen (1984) and J.P. Lhomme (personal communication, 1988) methods to obtain an uncoupled multi-layer model in order to estimate sensible and latent heat flux densities from a canopy in partially wet conditions, including heat conduction from the dry sublayer to the wet one. Chen's method gives the global Bowen ratio of the vegetation while Lhomme's method calculates the saturation deficit profile in the air and then the temperature differences between leaf surfaces and the air. Furthermore, we can obtain profiles of sensible and latent heat flux densities emanating from both wet and dry sublayers. Obviously the amount of water, Q(i), included in each layer decreases step by step depending on computed evaporation rates of wet surfaces. The SWD profile consists of a set of n - 1 values corresponding to the different durations when the n - 1 layers become dry. Using the first version of the model (no heat conduction from dry areas to water deposits), Huber ( 1988 ) presented a detailed analysis of the sensitivity to external variables and parameters. SWD increases with decreasing net radiation, saturation deficit or wind velocity. Concerning the leaf area index (LAI), there is an important increase in SWD with increasing LAI but SWD at the bottom of the canopy is not significantly influenced by the shape of the leaf area density profile.
Experimental conditions and measurements The experimental data were collected at the INRA Experimental Farm at La Mini~re near Versailles (France) during the summers of 1985 and 1986
286
L. HUBER AND B. ITIER
on a 1-ha field bean crop (Viciafaba). The rows were planted 0.3 m apart in a north-south orientation. The canopy height and the leaf area density profile were obtained from weekly measurements during the complete growing season. To avoid the difficulties of waiting for the occurrence of h u m i d and cloudy weather after a single continuous rainy event under low windspeed conditions during summer, wetness of the canopy was created by predawn sprinkling ( 30 sprinklers on 2500 m 2) under cloudy weather conditions. Concerning water storage capacity of a field bean crop, the maximal amount of water intercepted during sprinkling was determined by weighing, both under laboratory and field conditions. Micrometeorological measurements were taken at 2 m above the top of the canopy. Measured values were averaged every 15 min throughout the experiment. Net radiation was measured using Swissteco net radiometers and wind velocity was measured with optoelectronical MCB anemometers. Air and wet bulb temperatures were given by an automatic psychrometer using copper-constantan thermocouples (Seck and Perrier, 1970). An attempt was made to use impedance grids to characterize the SWD profile within the canopy, but in order to take into account the spatial variability we preferred visual assessment of the surface wetness duration in 2-4 canopy layers. The criterion used to define the SWD of any layer was that SWD was ended when at least 50% of a 30-leaf sample in the layer involved was completely dry. In fact, this represents the evaporation of more than 95% of the water amount initially stored in this layer. RESULTS Concerning the coefficient used to calculate the heat flux by conduction from dry areas to water deposits, Fig. 1 shows an example of simulated SWD at different heights in a 1.2 m height crop and assuming a beta distribution r ( 1.5,2 ) for the leaf area density profile (LAI = 8 ). Obviously, taking heat conduction into account reduces calculated surface wetness durations. That reduction is much higher at the bottom of the canopy. Using laboratory measurements of Butler ( 1985 ) for the value of the heat conduction coefficient (r/= 0.11 ) a reduction of 15% is observed in SWD at the bottom of the canopy when compared with the case without heat conduction (r/= 0). Increasing r/up to 0.25 W m - ~K - ~results in a 30% reduction of SWD at the bottom; in fact it corresponds to the situation where an increase of the heat conduction flux to the water deposits is compensated for by a decrease of the sensible heat flux. For the whole canopy in partially wet conditions and with r/= 0.11 W m - 1 K - 1, the heat conduction flux to water deposits represents 8-12% of the net radiation above the canopy. With forcing variables as indicated in Fig. 1, the different terms of the energy balance equations at the first time step of the simulation are given for both wet and dry parts of the canopy:
LEAFWETNESSDURATIONIN FIELDBEANCANOPY
287
ZidH( i,1) ,.,O W m -2 ,EidLE( i,1) = + l l 8 W m -2 2 ~ i 6 C ( i , 1 ) = - 1 8 W m -2 Zi~H( i,2 ) = + 1 8 W m -2 ZidLE( i,2 ) = + 6 4 W m -2 ZidC( i,2 ) = + 1 8 W m -2
The heat conduction from dry areas to water deposits tends to increase the temperature of the free water and then the saturated vapor pressure becomes higher so that the latent heat flux density of the wet sublayer may be higher than the available net radiation (equal to 100 W m - 2 for both wet and dry sublayers in this example). Figure 2 gives a global picture of correspondence between observed and computed values of SWD for a field bean crop. For all of these experimental days fl was taken equal to a value of 0 because water distribution on field bean leaves mostly corresponds to films or large flat drops. There is a fairly good agreement for the central and the bottom parts of the crop while the computed values of SWD for the upper part seem to be significantly overestimated. Concerning this disagreement, one point must be underlined: as experimental conditions correspond to artificial rain (sprinkling) on the crop while surrounding areas are dry, it is possible that local advection increases the evaporation rate of the top of the canopy and results in a shortening of the SWD compared with the case of natural rain. SWD of the upper part is shorter than for the middle and bottom parts of the canopy. In relation to disease prediction, it is usually more important to obtain good agreement for long surface wetness durations that will occur within the canopy. Taking heat conRn = 2 0 0 W . r n
-z
,11
Td = 12°C
TO
= 15°C
V
= 2 rn.s "1
1.2
1.0
~
0.25
x11 =
0.2
,'q
0.1
=
o'11 =
0.06
,.1]
o. o4
=
0.8
-/ N
=
0.6
0.4
0.2. o SWD
(h)
Fig. l. Simulated profiles o f surface wetness duration ( S W D ) in a field bean crop (h = 1.2 m; LAI = 8) using different values for the heat conduction coefficient ( f r o m 0 to 0.25 W m - ~ K - l ) and keeping the external variables as steady-state values.
288
L. H U B E R AND B. ITIER
O
1.2~
162 / 8 5
~
O 165 / 8 5
1.0.
,
D
170
/85
0.8. N 0.6. 0.4. 0120
,
J
,
i
i
i
J
O 176 / 8 5
1.2
i
i
~
"•,,
1.4
1.0 E
_k_~~"',,,
\\\x_
0.8. o.6_
i
1
i
D 177/85
i
i
i
i
i
D 179/85
i
0.4_ 0.2_ 0 0
,
/
I
2
i
i
i
i
i
3
4
5
6
7
SWD (h) D
~
SWD (h)
175/86
O
s w o (h)
182 / 8 6
1.2_ 1.0. 0.8 N
0.6+ 0.4.
0"20! ¢'
,
/86
i
0
swo
(h)
SWD
(h}
SWD (h)
Fig. 2. Simulated profiles of SWD for 9 days (summers 1985 and 1986) in a 1.2 m height crop of field beans for three values of the heat conduction coefficient (- - -, r/= 0; , ~/= 0.11; - - - , r/= 0.25) vs. a visual assessment (I--I: assessed time interval corresponding to drying of 25% and 75% of wetted leaves in a 30-leafsample in the layer). The water distribution parameter (#) is kept equal to 0 (case of a continuous water film).
duction into account improves the global correspondence between observed and simulated values. For the bottom of the canopy, correlation coefficients between assessed and predicted values are 0.59, 0.66 and 0.71, respectively, with r/=0, 0.11 and 0.25 W m -~ K -1. Figure 3 gives a comparison of assessed and computed values of SWD for the lower levels inside the crop, depending on the value of the water distribution parameter (fl). The horizontal line represents the time interval corresponding to drying of 25% and 75% of wetted leaves (see above) and vertical lines represent the differences in simulated SWD for three values of the con-
LEAFWETNESSDURATIONIN FIELDBEANCANOPY
289
10/
-g
/
0
g)
4_ 2_
/ / / /
o 0
I 2
I
E
4
6
i 8
I 10
SWDa ( h o u r s ) ,~ : p : o
o : ~=tla
• :,e=z/a
Fig. 3. Comparison between predicted and assessed results of SWD for the bottom layer inside the canopy in relation to the water distribution parameter (fl). Horizontal lines represent the assessed time intervals corresponding to drying of 25% and 75% of wetted leaves. Vertical lines represent the differences in simulated SWD for three values of the water distribution parameter (fl=0; 1/3; 2/3). The heat conduction coefficient (;7) is kept equal to 0.11 W m - ~K - 1.
duction coefficient (fl). The influence of water distribution on leaves is not at all negligible: from r = 0 (which represents the case of a constant area covering the leaves as a water film ) to fl = 2 / 3 (which represents the case of evaporation of hemispherical drops keeping their shape constant throughout the experiment) the SWD can be increased by a factor of two at the bottom of the canopy. Regarding the parameterization of water distribution, Fig. 3 shows that a good agreement between calculated and assessed values of SWD is obtained with r = 0 and r/= 0.11 W m-1 K-1 (correlation coefficients between calculated and assessed values are 0.66, 0.53 and 0.1 l, respectively, with r = 0, 1/3 and 2/3). DISCUSSION AND CONCLUSIONS
The present work deals with the influence of heat conduction from dry surfaces of leaves to intercepted water deposits in the framework of a soil-plantatmosphere model devoted to simulation of surface wetness duration profiles. Butler ( 1985 ) pointed out the significant role played by heat conduction when modelling eyaporation of isolated drops under controlled conditions. This author found that "the effect of heat conduction would be to increase the drop evaporation rate by about 40%"; in the case of wetted leaves in the bottom of a crop canopy we estimate an increase of about the same percentage for the evaporation rate of water deposits owing to rain interception un-
290
L. HUBER AND B. ITIER
der field conditions. Compared with the simulation model of Butler ( 1986 ), the method proposed in this paper makes it unnecessary to solve differential equations; furthermore, field tests of performance are presented for 10 days. Barr and Gillespie ( 1987 ) observed that estimates of SWD for water drops placed on shaded corn leaves at the bottom of the canopy were significantly higher than observed SWD for more than 50% of the drops: taking heat conduction into account could diminish the discrepancy. To go further it would probably be necessary to improve some parameterizations (radiation profile in the canopy for instance ) and incorporate other physical processes. In spite of the added complexity which will result, considering drop size distribution would be interesting. Brain and Butler (1985) did this in a one-layer model to simulate evaporation of a population of drops using an initial log-normal distribution, but they did not include heat conduction between drops and the leaf. Another improvement would be to govern the heat and mass transfers of water drops using the drop diameter as a characteristic dimension (Leclerc et al., 1985). The model presented shows the importance of heat conduction in order to estimate SWD in the lower part of the canopy. This fact differs somewhat from the conclusion of Leclerc et al. ( 1985 ) who worked with artificial soybean leaves and assumed negligible net radiation. In contrast, the weak influence of heat conduction on SWD at the upper part of the canopy agrees well with the assumption of Gillespie and Duan (1987 ). They did not take heat conduction into account in computing SWD of drops placed on sensors tested in a wind tunnel at different wind speeds. They observed some discrepancy between computed and observed values for a cylindrical sensor but negligible discrepancy for a fiat sensor and concluded that "conduction of heat to the drops through the cylinder is significant at low wind speeds" but that "most fiat leaves are too thin to conduct significant heat to the drop". In both cases SWD was less than 100 min. However in the case of long SWD at the bottom of the canopy, it is established that heat conduction plays an effective role in the energy balance of water deposits on fiat leaves.
REFERENCES Avissar, R., Avissar, P., Mahrer, Y. and Bravdo, B.A., 1985. A model to simulate response of plant stomata to environmental conditions. Agric. For. Meteorol., 34:21-29. Barr, A. and Gillespie, T.J., 1987. Maximum wetness duration for water drops on leaves in the field. Agric. For. Meteorol., 41: 267-274. Brain, P. and Butler, D.R., 1985. A model of drop size distribution for a system with evaporation. Plant Cell Environ., 8: 247-252. Butler, D.R., 1985. The energy balance of water drops on a leaf surface. Boundary Layer Meteorol., 32: 337-350. Butler, D.R., 1986. Evaporation from rain drops on leaves in a cereal canopy: a simulatioo model. Boundary Layer Meteorol., 36: 39-52.
LEAF WETNESS DURATION IN FIELD BEAN CANOPY
291
Chen, J., 1984. Mathematical analysis and simulation of crop micrometeorology. Thesis, Wageningen, 116 pp. Crowe, M.J., Coakley, S.M. and Emge, R.G., 1978. Forecasting dew duration at Pendleton, Oregon using simple weather observations. J. Appl. Meteorol., 17:1482-1487. Finnigan, J.J. and Raupach, M.R., 1987. Transfer processes in plant canopies in relation to stomatal characteristics. In: E. Zeiger, G. Farquhar, I. Cowan (Editors), Stomatal Function. Stanford University Press, Stanford CA, pp. 385-429. Gillespie, T.J. and Duan, R.X., 1987. A comparison of cylindrical and fiat plate sensors for surface wetness duration. Agric. For. Meteorol., 40:61-70. Gillespie, T.J. and Kidd, G.E., 1978. Sensing duration of leaf moisture retention using electrical impedance grids. Can. J. Plant Sci., 58: 179-187. Gillespie, T.J. and Sutton, J.C., 1979. A predictive scheme for timing fungicide applications to control alternaria leaf blight in carrots. Can. J. Plant Pathol., 1: 95-99. Goudriaan, J., 1977. Crop micrometeorology: a simulation study. Simulation monographs, Pudoc, Wageningen, 249 pp. H~ickel, H., 1980. Neues fiber die elektrische Methode zur Messung der Benetzungsdauer unmittelbar an der Pflanze. Agric. Meteorol., 22:113-119. H~ickel, H., 1984. Zur Messung der Benetzungsdauer von Pflanzen: Verfahren und Ergebnisse. Meteorol. Rundsch., 37: 97-104. Huband, N.D.S. and Butler, D.R., 1984. A comparison of wetness sensors for use with computer or microprocessor systems designed for disease forecasting. In: Proc. British crop protection Conf. on pests and diseases, BCPC, Croydon, Vol. II, pp. 633-638. Huber, L., 1988. ModUle de simulation de la dur6e d'humectation des feuilles au champ apr~s une pluie. Cas d'un couvert homogbne. Agronomie, 8: 675-684. Huber, L. and Wehrlen, J.M., 1988. La dur6e d'humectation en protection des plantes: mesure et mod61isation. Def. Veg., 252:3-11. Impens, 1. and Lemeur, R., 1969. Extinction of net radiation in different crop canopies. Arch. Meteorol. Geophys. Bioklimatol., Ser. B, 17: 403-412. Jones, A.L., 1986. Role of wet periods in predicting foliar diseases. In: K.J. Leonard and W.E. Fry (Editors), Plant Disease Epidemiology, Vol. 1: Population Dynamics and Management. Macmillan, New York, NY, pp. 87-100. Landsberg, J.J. and James, G.B., 1971. Wind profiles in plant canopies: studies on an analytical model. J. Appl. Ecol., 8: 729-741. Leclerc, M.Y., Thurtell, G.W. and Gillespie, T.J., 1985. Laboratory simulation of evaporation of water droplets on artificial soybean leaves. Agric. For. Meteorol., 36:105-112. Monteith, J.L. and Butler, D.R., 1979. Dew and thermal lag: a model for cocoa pods. Q. J.R. Meteorol. Soc., 105:207-215. Norman, J.M., 1979. Modeling the complete crop canopy. In: B. Hatfield and J. Gerber (Editors), Modification of the Aerial Environment of Crops. ASAE Monogr. No. 262, St Joseph, MI, pp. 249-277. Payen, D., 1983. Mod61isation de l'6pid6miologie de Sclerotinia sclerotiorum sur Tournesol. Bull. O.E.P.P., 13: 272-281. Pedro, M.J. and Gillespie, T.J., 1982. Estimating dew duration. I. Utilizing micrometeorological data. Agric. Meteorol., 25: 283-296. Rotem, J., 1988. Techniques of controlled-condition experiments. In: J. Kranz and J. Rotem (Editors), Experimental Techniques in Plant Disease Epidemiology. Springer Verlag, Berlin, Chapter 2, pp. 19-32. Seck, M. and Perrier, A., 1970. Description d'un psychrom~tre a thermocouples. Son application h la mesure des gradients d'humidit6. In: Techniques d'6tude des Facteurs Physiques de la Biosphere. INRA, Paris, pp. 223-234.
292
L. HUBER AND B. IT1ER
Shuttleworth, W.J. and Wallace, J.S., 1985. Evaporation from sparse crops - an energy combination theory. Q. J.R. Meteorol. Soc., 111: 839-855. Sutton, J.C., Gillespie, T.J. and James, T.D.W., 1988. Electronic monitoring and use of microprocessors in the field. In: J. Kranz and J. Rotem (Editors), Experimental Techniques in Plant Disease Epidemiology. Springer Verlag, Berlin, Chapter 7, pp. 99-113. Thom, A.S., 1971. Momentum absorption by vegetation. Q. J.R. Meteorol. Soc., 97:414-428. Thompson, N., 1981. The duration of leaf wetness. Meteorol. Mag., 110: 1-12. Van der Wal, A.F., 1978. Moisture as a factor in epidemiology and forecasting. In: T.T. Kozlowski (Editor), Water Deficits and Plant Growth, Vol. 5: Water and Plant Disease. Academic Press, New York, NY, pp. 253-295. Weiss, A. and Hagen, F.A., 1983. Further experiments on the measurements of leaf wetness. Agric. Meteorol., 29:207-212. Weiss, A. and Norman, J.M., 1987. Comparison of field measurements and numerical simulations of leaf wetness durations in a dry bean canopy. In: 18th Conference Agriculture and Forest Meteorology, American Meteorological Society, West Lafayette, IN, 15-18 September 1987, J4.3, pp. 52-53.
281
Elsevier Science Publishers B.V., A m s t e r d a m - - Printed in The Netherlands
Leaf wetness duration in a field bean canopy L. Huber and B. Itier Institut National de la Recherche Agronomique, Centre de Recherches de Grignon-Massy-Paris, Station de Bioclimatologie, F - 78850 Thiverval-Grignon (France} (Received July 8, 1989; revision accepted January 4, 1990)
ABSTRACT Huber, L. and Itier, B., 1990. Leaf wetness duration in a field bean canopy. Agric. For. Meteoroi., 51: 281-292. The experimental testing of a multi-layer model to simulate surface wetness duration (SWD) in a canopy is presented. A previous model was modified by includingthe heat conduction from dry areas of leaves to water deposits. Field tests after sprinkling during humid and cloudy weather are reported for 10 days in the summers of 1985 and 1986. The discussion is focused on the importance of heat conduction and the influence of water distribution on leaves in determining SWD.
INTRODUCTION
Surface wetness duration (SWD) is an important factor in agriculture, not only for cultural practices such as harvesting or hay drying but also for the biological cycles of pests (Van der Wal, 1978 ). In disease predictive schemes, the influence of SWD on infection phases is commonly determined under controlled conditions (Rotem, 1988 ). To obtain an estimate of SWD in the field, several methods have been investigated: either a calculation using local relationships between SWD and meteorological variables (Crowe et al., 1978; Gillespie and Sutton, 1979) or using direct measurements of SWD by means of appropriate sensors (Gillespie and Kidd, 1978; H~ickel, 1980, 1984; Weiss and Hagen, 1983; Gillespie and Duan, 1987 ). Jones ( 1986 ) and Sutton et al. ( 1988 ) reviewed different types of sensors. Measured values of SWD are highly dependent on the type of sensor used (Weiss and Hagen, 1983; Huband and Butler, 1984 ). Furthermore, a good description of SWD in the field would need a large number of sensors to account for the high variability (Huber and Wehrlen, 1988 ). Hence, attempts have been made to build deterministic models in order to simulate SWD using standard weather station data or micrometeorological data. Beside simple models devoted to SWD estimates of particular organs or canopy positions (Monteith and Butler, 1979; Pedro and Gillespie, 1982; 0168-1923/90/$03.50
© 1990 Elsevier Science Publishers B.V.
282
L. HUBER AND B. ITIER
Payen, 1983), multi-layer models have been proposed to simulate the leaf wetness duration profile within the canopy in cases of rain or dew (Goudriaan, 1977; Norman, 1979; Thompson, 1981; Butler, 1986). None of these approaches, excepted Butler's model, include heat conduction from the dry parts to the wetted parts of leaves. Only two models have been tested under field conditions: Weiss and Norman (1987) have presented field tests of the CUPID model (Norman, 1979) under dew conditions for 5 days; Butler (1986) has only presented a l-day comparison in the case of wetness due to rain. The aim of this paper is to present the experimental tests under field conditions of a multi-layer model, including heat conduction, to simulate the SWD profile after a rain event using a set of data obtained during 10 days. METHODS
Model The SWD profile was simulated using a steady state one-dimensional multilayer model. A previous model (Huber, 1988) was modified to take into account the heat conduction from dry areas to water deposits on leaves of a partially wet canopy. External variables are air temperature, dew-point, wind velocity and net radiation measured at a reference height, i.e. 2 m above the top of the canopy. The plant canopy is assumed to be horizontally uniform and its structure is described by means of a leaf area density profile, the mean height of the plants and a characteristic dimension of leaves. The windspeed profile u (z) within the crop is simulated using an analytical expression as proposed by Landsberg and James ( 1971 ):
u(z)=u(h) [ l + a ( 1 - z / h ) ] - 2 where a = 1.3, h is the height of the canopy and z the height above the soil. The turbulent exchanges in the air are described using K-theory. The turbulent diffusivity profile K(z) above and within the canopy varies as proposed by Thorn ( 1971 ) for field beans:
:K(z)=ku* ( z - d ) where d=0.75 h for h/3
for z > h
k is the yon Karman's constant (0.4), u , the friction velocity and d is the height of the zero plane displacement. Owing to low net radiation levels and low values of Bowen ratio, the aerodynamic resistance Ra above the canopy is computed using a forced convection formula:
283
LEAF W E T N E S S D U R A T I O N IN F I E L D BEAN C A N O P Y
Ra= (k u , ) - ' Ln[ ( z ~ f - d ) / ( h - d ) ] where Zref is the reference height above the canopy where the forcing variables are measured. For the same reason, exchange coefficients of both wet and dry parts of leaves are computed as a function of their Nusselt number (Nu). The characteristic dimension used for computing Nu corresponds to the mean width of leaves. The Nusselt number is computed as proposed by Finnigan and Raupach ( 19 8 7 ) using Reynolds (Re) and Prandtl (Pr = 0.7 ) numbers: N u = 1.3 Re I/2 Pr ~/3 To govern the evapotranspiration process on so-called dry parts of leaf surfaces, the stomatal resistance profile Rs(z) was determined using the global radiation profile Rg ( z ) (Avissar et al., 19 8 5 ):
ifO
Rs(z)-l-Rsmlax --1
RS m i n
--1
--
Rs m a x
--
Rg(z)-Rginf Rgsup- Rginf
if Rgsup< Rg(z) then Rs(z) =RSmin Shown in these equations are the minimal and maximal stomatal resistances (RSmin and Rsmax) corresponding respectively to two thresholds of global radiation (Rgsup and Rginf). The soil-plant system is divided in n - 1 horizontal layers and a soil layer. Every layer of the canopy is divided into two sublayers: a wetted sublayer and a dry sublayer. Only the upward leaf surface may be wetted during a rainy event (it would be different in the case of dew because of condensation upon both leaf surfaces). The energy balance equation for each sublayer j ( j = 1: wet sublayer; j = 2: dry sublayer) of a canopy layer i ( 1 < i < n - 1 ) is given by:
W(i,j) ~Rn(i) =~H(i,j) +#LE(i,j) +#C(i,j) where W(i,j) is the absorbed fraction of available energy ~Rn (i) by sublayer j in layer i, and ~H(i,j) and ~LE(i,j) are respectively the sensible heat flux and latent heat flux densities emanating for both sublayers. ~C(i,j) is the heat conduction flux density (from the dry parts to the water deposits for j = 2 and inversely for j = 1 ). ~H(i,j), ~LE(i,j) and ~C(i,j) are given by the following expressions:
284
L. HUBER AND B. ITIER
OH( i,j) =p Cp hh( i,j) [ Ts( i , j ) - Ta( i) ] OLE( i,j) =? Cp hv( i,j) {es[ Ts( i,j) ] -ea( i) }/v OC( i,j) = 0 ( j ) k( i) [ Ts( i,2 ) - Ts( i, 1 ) ] where 0(j) = + 1 if j = 1 and 0(j) = - 1 if j = 2 and k( i) =2 ~z1/2 q [ W( i) LAI(i) Nw( i) Nl( i) ]1/2 Symbols in these equations are the air density (p), specific heat of air at constant pressure (Cp), psychrometric constant (~), saturated vapor density function (es(T) ) and the heat conduction coefficient (q). Ts(i,j) is the surface temperature of the sublayer j in the layer i, Ta (i) and ea (i) are the air temperature and the vapor pressure in the layer i; hh(i,j) and hv(i,j) are the exchange coefficients for heat and vapor transfer respectively and are expressed as functions of the computed Nu, stomatal resistance and wetted area percentage of each layer. LAI (i) corresponds to the fraction of LAI in the layer i and W(i) is defined as the wetted area percentage ( W ( i ) = 1 if the leaves of the layer i are completely wet on the upper side). Nw(i) is the number of individual wet surfaces per leaf, Nl(i) is the number of leaves in the layer i. The expression for the coefficient k (i) is obtained by assuming that the conduction flux is proportional to the total circumference of the individual wet surfaces in the layer i, as proposed by Butler ( 1985 ) who obtained an estimate of the effective thermal conductivity coefficient in the case of heat conduction to an isolated drop of water on a wheat leaf. For sensitivity analysis purposes, q was allowed to vary from 0 to 0.25 W m-1 K-1. The mean value obtained by Butler on winter wheat leaves is equal to 0.11 W m - 1 K- 1. For the soil layer n there is only one energy balance equation:
ORn ( n ) = 0 H ( n ) + OLE ( n ) To take into account the soil contributions OH(n) and OLE(n) to sensible heat flux and latent heat flux densities, we assume exchange coefficients hh (n) and hv (n) as proposed by Goudriaan ( 1977 ) and a surface resistance as proposed by Shuttleworth and Wallace ( 1985 ). The available net radiation ORn (i) in layer i is computed using Impens and Lemeur ( 1969): if 1 < i < n - 1: ORn(i)=Rn(h) { e x p [ - K F ( i - l ) ] - e x p [ - K F ( i ) ] } if i = n: ORn(n) =Rn(h) exp[ - K F ( n - 1 ) ] - G where K is the extinction coefficient ( K = 0 . 5 for overcast days), F(i) the cumulative leaf area density function from the top of the canopy to the bottom of layer i and G is the conduction heat flux into the ground estimated as 20% of the net radiation available in the layer n - 1. The partitioning of the
LEAF WETNESS DURATION IN FIELD BEAN CANOPY
285
available net radiation ~Rn (i) in a given canopy layer between both wet and dry sublayers linearly depends on wetted area percentage W(i) in the layer involved:
W( i,1 ) = W( i) /2 and W(i,2) = l - W( i) /2 Initial conditions required for the model are the surface water storage of the canopy (S) and the initial value Wo (i) of the wet area percentage ( W ( i ) ) in each layer i. The initial value of W(i) is assumed to be the same (Wo) in each layer i. The time evolutions of the wet area percentage W(i) and the water amount on the leaves Q (i) in each layer i are computed at the end of every time step by means of (Huber, 1988 ):
W( i) / Wo= [Q( i) / Qo( i) ]P where: Qo( i) = Wo( i) (S/LAI) LAI(i) The exponent fl depends on surface water distribution (fl=0 for water films with constant wetted area, fl= 2/3 for hemispheric shaped drops). Following Butler's ( 1985 ) laboratory experiments the coefficient (r/) for heat transfer by conduction from wet to dry parts of leaves was kept constant throughout the wetness duration and independent of changes in the size of wet areas. The numerical procedure uses both Chen (1984) and J.P. Lhomme (personal communication, 1988) methods to obtain an uncoupled multi-layer model in order to estimate sensible and latent heat flux densities from a canopy in partially wet conditions, including heat conduction from the dry sublayer to the wet one. Chen's method gives the global Bowen ratio of the vegetation while Lhomme's method calculates the saturation deficit profile in the air and then the temperature differences between leaf surfaces and the air. Furthermore, we can obtain profiles of sensible and latent heat flux densities emanating from both wet and dry sublayers. Obviously the amount of water, Q(i), included in each layer decreases step by step depending on computed evaporation rates of wet surfaces. The SWD profile consists of a set of n - 1 values corresponding to the different durations when the n - 1 layers become dry. Using the first version of the model (no heat conduction from dry areas to water deposits), Huber ( 1988 ) presented a detailed analysis of the sensitivity to external variables and parameters. SWD increases with decreasing net radiation, saturation deficit or wind velocity. Concerning the leaf area index (LAI), there is an important increase in SWD with increasing LAI but SWD at the bottom of the canopy is not significantly influenced by the shape of the leaf area density profile.
Experimental conditions and measurements The experimental data were collected at the INRA Experimental Farm at La Mini~re near Versailles (France) during the summers of 1985 and 1986
286
L. HUBER AND B. ITIER
on a 1-ha field bean crop (Viciafaba). The rows were planted 0.3 m apart in a north-south orientation. The canopy height and the leaf area density profile were obtained from weekly measurements during the complete growing season. To avoid the difficulties of waiting for the occurrence of h u m i d and cloudy weather after a single continuous rainy event under low windspeed conditions during summer, wetness of the canopy was created by predawn sprinkling ( 30 sprinklers on 2500 m 2) under cloudy weather conditions. Concerning water storage capacity of a field bean crop, the maximal amount of water intercepted during sprinkling was determined by weighing, both under laboratory and field conditions. Micrometeorological measurements were taken at 2 m above the top of the canopy. Measured values were averaged every 15 min throughout the experiment. Net radiation was measured using Swissteco net radiometers and wind velocity was measured with optoelectronical MCB anemometers. Air and wet bulb temperatures were given by an automatic psychrometer using copper-constantan thermocouples (Seck and Perrier, 1970). An attempt was made to use impedance grids to characterize the SWD profile within the canopy, but in order to take into account the spatial variability we preferred visual assessment of the surface wetness duration in 2-4 canopy layers. The criterion used to define the SWD of any layer was that SWD was ended when at least 50% of a 30-leaf sample in the layer involved was completely dry. In fact, this represents the evaporation of more than 95% of the water amount initially stored in this layer. RESULTS Concerning the coefficient used to calculate the heat flux by conduction from dry areas to water deposits, Fig. 1 shows an example of simulated SWD at different heights in a 1.2 m height crop and assuming a beta distribution r ( 1.5,2 ) for the leaf area density profile (LAI = 8 ). Obviously, taking heat conduction into account reduces calculated surface wetness durations. That reduction is much higher at the bottom of the canopy. Using laboratory measurements of Butler ( 1985 ) for the value of the heat conduction coefficient (r/= 0.11 ) a reduction of 15% is observed in SWD at the bottom of the canopy when compared with the case without heat conduction (r/= 0). Increasing r/up to 0.25 W m - ~K - ~results in a 30% reduction of SWD at the bottom; in fact it corresponds to the situation where an increase of the heat conduction flux to the water deposits is compensated for by a decrease of the sensible heat flux. For the whole canopy in partially wet conditions and with r/= 0.11 W m - 1 K - 1, the heat conduction flux to water deposits represents 8-12% of the net radiation above the canopy. With forcing variables as indicated in Fig. 1, the different terms of the energy balance equations at the first time step of the simulation are given for both wet and dry parts of the canopy:
LEAFWETNESSDURATIONIN FIELDBEANCANOPY
287
ZidH( i,1) ,.,O W m -2 ,EidLE( i,1) = + l l 8 W m -2 2 ~ i 6 C ( i , 1 ) = - 1 8 W m -2 Zi~H( i,2 ) = + 1 8 W m -2 ZidLE( i,2 ) = + 6 4 W m -2 ZidC( i,2 ) = + 1 8 W m -2
The heat conduction from dry areas to water deposits tends to increase the temperature of the free water and then the saturated vapor pressure becomes higher so that the latent heat flux density of the wet sublayer may be higher than the available net radiation (equal to 100 W m - 2 for both wet and dry sublayers in this example). Figure 2 gives a global picture of correspondence between observed and computed values of SWD for a field bean crop. For all of these experimental days fl was taken equal to a value of 0 because water distribution on field bean leaves mostly corresponds to films or large flat drops. There is a fairly good agreement for the central and the bottom parts of the crop while the computed values of SWD for the upper part seem to be significantly overestimated. Concerning this disagreement, one point must be underlined: as experimental conditions correspond to artificial rain (sprinkling) on the crop while surrounding areas are dry, it is possible that local advection increases the evaporation rate of the top of the canopy and results in a shortening of the SWD compared with the case of natural rain. SWD of the upper part is shorter than for the middle and bottom parts of the canopy. In relation to disease prediction, it is usually more important to obtain good agreement for long surface wetness durations that will occur within the canopy. Taking heat conRn = 2 0 0 W . r n
-z
,11
Td = 12°C
TO
= 15°C
V
= 2 rn.s "1
1.2
1.0
~
0.25
x11 =
0.2
,'q
0.1
=
o'11 =
0.06
,.1]
o. o4
=
0.8
-/ N
=
0.6
0.4
0.2. o SWD
(h)
Fig. l. Simulated profiles o f surface wetness duration ( S W D ) in a field bean crop (h = 1.2 m; LAI = 8) using different values for the heat conduction coefficient ( f r o m 0 to 0.25 W m - ~ K - l ) and keeping the external variables as steady-state values.
288
L. H U B E R AND B. ITIER
O
1.2~
162 / 8 5
~
O 165 / 8 5
1.0.
,
D
170
/85
0.8. N 0.6. 0.4. 0120
,
J
,
i
i
i
J
O 176 / 8 5
1.2
i
i
~
"•,,
1.4
1.0 E
_k_~~"',,,
\\\x_
0.8. o.6_
i
1
i
D 177/85
i
i
i
i
i
D 179/85
i
0.4_ 0.2_ 0 0
,
/
I
2
i
i
i
i
i
3
4
5
6
7
SWD (h) D
~
SWD (h)
175/86
O
s w o (h)
182 / 8 6
1.2_ 1.0. 0.8 N
0.6+ 0.4.
0"20! ¢'
,
/86
i
0
swo
(h)
SWD
(h}
SWD (h)
Fig. 2. Simulated profiles of SWD for 9 days (summers 1985 and 1986) in a 1.2 m height crop of field beans for three values of the heat conduction coefficient (- - -, r/= 0; , ~/= 0.11; - - - , r/= 0.25) vs. a visual assessment (I--I: assessed time interval corresponding to drying of 25% and 75% of wetted leaves in a 30-leafsample in the layer). The water distribution parameter (#) is kept equal to 0 (case of a continuous water film).
duction into account improves the global correspondence between observed and simulated values. For the bottom of the canopy, correlation coefficients between assessed and predicted values are 0.59, 0.66 and 0.71, respectively, with r/=0, 0.11 and 0.25 W m -~ K -1. Figure 3 gives a comparison of assessed and computed values of SWD for the lower levels inside the crop, depending on the value of the water distribution parameter (fl). The horizontal line represents the time interval corresponding to drying of 25% and 75% of wetted leaves (see above) and vertical lines represent the differences in simulated SWD for three values of the con-
LEAFWETNESSDURATIONIN FIELDBEANCANOPY
289
10/
-g
/
0
g)
4_ 2_
/ / / /
o 0
I 2
I
E
4
6
i 8
I 10
SWDa ( h o u r s ) ,~ : p : o
o : ~=tla
• :,e=z/a
Fig. 3. Comparison between predicted and assessed results of SWD for the bottom layer inside the canopy in relation to the water distribution parameter (fl). Horizontal lines represent the assessed time intervals corresponding to drying of 25% and 75% of wetted leaves. Vertical lines represent the differences in simulated SWD for three values of the water distribution parameter (fl=0; 1/3; 2/3). The heat conduction coefficient (;7) is kept equal to 0.11 W m - ~K - 1.
duction coefficient (fl). The influence of water distribution on leaves is not at all negligible: from r = 0 (which represents the case of a constant area covering the leaves as a water film ) to fl = 2 / 3 (which represents the case of evaporation of hemispherical drops keeping their shape constant throughout the experiment) the SWD can be increased by a factor of two at the bottom of the canopy. Regarding the parameterization of water distribution, Fig. 3 shows that a good agreement between calculated and assessed values of SWD is obtained with r = 0 and r/= 0.11 W m-1 K-1 (correlation coefficients between calculated and assessed values are 0.66, 0.53 and 0.1 l, respectively, with r = 0, 1/3 and 2/3). DISCUSSION AND CONCLUSIONS
The present work deals with the influence of heat conduction from dry surfaces of leaves to intercepted water deposits in the framework of a soil-plantatmosphere model devoted to simulation of surface wetness duration profiles. Butler ( 1985 ) pointed out the significant role played by heat conduction when modelling eyaporation of isolated drops under controlled conditions. This author found that "the effect of heat conduction would be to increase the drop evaporation rate by about 40%"; in the case of wetted leaves in the bottom of a crop canopy we estimate an increase of about the same percentage for the evaporation rate of water deposits owing to rain interception un-
290
L. HUBER AND B. ITIER
der field conditions. Compared with the simulation model of Butler ( 1986 ), the method proposed in this paper makes it unnecessary to solve differential equations; furthermore, field tests of performance are presented for 10 days. Barr and Gillespie ( 1987 ) observed that estimates of SWD for water drops placed on shaded corn leaves at the bottom of the canopy were significantly higher than observed SWD for more than 50% of the drops: taking heat conduction into account could diminish the discrepancy. To go further it would probably be necessary to improve some parameterizations (radiation profile in the canopy for instance ) and incorporate other physical processes. In spite of the added complexity which will result, considering drop size distribution would be interesting. Brain and Butler (1985) did this in a one-layer model to simulate evaporation of a population of drops using an initial log-normal distribution, but they did not include heat conduction between drops and the leaf. Another improvement would be to govern the heat and mass transfers of water drops using the drop diameter as a characteristic dimension (Leclerc et al., 1985). The model presented shows the importance of heat conduction in order to estimate SWD in the lower part of the canopy. This fact differs somewhat from the conclusion of Leclerc et al. ( 1985 ) who worked with artificial soybean leaves and assumed negligible net radiation. In contrast, the weak influence of heat conduction on SWD at the upper part of the canopy agrees well with the assumption of Gillespie and Duan (1987 ). They did not take heat conduction into account in computing SWD of drops placed on sensors tested in a wind tunnel at different wind speeds. They observed some discrepancy between computed and observed values for a cylindrical sensor but negligible discrepancy for a fiat sensor and concluded that "conduction of heat to the drops through the cylinder is significant at low wind speeds" but that "most fiat leaves are too thin to conduct significant heat to the drop". In both cases SWD was less than 100 min. However in the case of long SWD at the bottom of the canopy, it is established that heat conduction plays an effective role in the energy balance of water deposits on fiat leaves.
REFERENCES Avissar, R., Avissar, P., Mahrer, Y. and Bravdo, B.A., 1985. A model to simulate response of plant stomata to environmental conditions. Agric. For. Meteorol., 34:21-29. Barr, A. and Gillespie, T.J., 1987. Maximum wetness duration for water drops on leaves in the field. Agric. For. Meteorol., 41: 267-274. Brain, P. and Butler, D.R., 1985. A model of drop size distribution for a system with evaporation. Plant Cell Environ., 8: 247-252. Butler, D.R., 1985. The energy balance of water drops on a leaf surface. Boundary Layer Meteorol., 32: 337-350. Butler, D.R., 1986. Evaporation from rain drops on leaves in a cereal canopy: a simulatioo model. Boundary Layer Meteorol., 36: 39-52.
LEAF WETNESS DURATION IN FIELD BEAN CANOPY
291
Chen, J., 1984. Mathematical analysis and simulation of crop micrometeorology. Thesis, Wageningen, 116 pp. Crowe, M.J., Coakley, S.M. and Emge, R.G., 1978. Forecasting dew duration at Pendleton, Oregon using simple weather observations. J. Appl. Meteorol., 17:1482-1487. Finnigan, J.J. and Raupach, M.R., 1987. Transfer processes in plant canopies in relation to stomatal characteristics. In: E. Zeiger, G. Farquhar, I. Cowan (Editors), Stomatal Function. Stanford University Press, Stanford CA, pp. 385-429. Gillespie, T.J. and Duan, R.X., 1987. A comparison of cylindrical and fiat plate sensors for surface wetness duration. Agric. For. Meteorol., 40:61-70. Gillespie, T.J. and Kidd, G.E., 1978. Sensing duration of leaf moisture retention using electrical impedance grids. Can. J. Plant Sci., 58: 179-187. Gillespie, T.J. and Sutton, J.C., 1979. A predictive scheme for timing fungicide applications to control alternaria leaf blight in carrots. Can. J. Plant Pathol., 1: 95-99. Goudriaan, J., 1977. Crop micrometeorology: a simulation study. Simulation monographs, Pudoc, Wageningen, 249 pp. H~ickel, H., 1980. Neues fiber die elektrische Methode zur Messung der Benetzungsdauer unmittelbar an der Pflanze. Agric. Meteorol., 22:113-119. H~ickel, H., 1984. Zur Messung der Benetzungsdauer von Pflanzen: Verfahren und Ergebnisse. Meteorol. Rundsch., 37: 97-104. Huband, N.D.S. and Butler, D.R., 1984. A comparison of wetness sensors for use with computer or microprocessor systems designed for disease forecasting. In: Proc. British crop protection Conf. on pests and diseases, BCPC, Croydon, Vol. II, pp. 633-638. Huber, L., 1988. ModUle de simulation de la dur6e d'humectation des feuilles au champ apr~s une pluie. Cas d'un couvert homogbne. Agronomie, 8: 675-684. Huber, L. and Wehrlen, J.M., 1988. La dur6e d'humectation en protection des plantes: mesure et mod61isation. Def. Veg., 252:3-11. Impens, 1. and Lemeur, R., 1969. Extinction of net radiation in different crop canopies. Arch. Meteorol. Geophys. Bioklimatol., Ser. B, 17: 403-412. Jones, A.L., 1986. Role of wet periods in predicting foliar diseases. In: K.J. Leonard and W.E. Fry (Editors), Plant Disease Epidemiology, Vol. 1: Population Dynamics and Management. Macmillan, New York, NY, pp. 87-100. Landsberg, J.J. and James, G.B., 1971. Wind profiles in plant canopies: studies on an analytical model. J. Appl. Ecol., 8: 729-741. Leclerc, M.Y., Thurtell, G.W. and Gillespie, T.J., 1985. Laboratory simulation of evaporation of water droplets on artificial soybean leaves. Agric. For. Meteorol., 36:105-112. Monteith, J.L. and Butler, D.R., 1979. Dew and thermal lag: a model for cocoa pods. Q. J.R. Meteorol. Soc., 105:207-215. Norman, J.M., 1979. Modeling the complete crop canopy. In: B. Hatfield and J. Gerber (Editors), Modification of the Aerial Environment of Crops. ASAE Monogr. No. 262, St Joseph, MI, pp. 249-277. Payen, D., 1983. Mod61isation de l'6pid6miologie de Sclerotinia sclerotiorum sur Tournesol. Bull. O.E.P.P., 13: 272-281. Pedro, M.J. and Gillespie, T.J., 1982. Estimating dew duration. I. Utilizing micrometeorological data. Agric. Meteorol., 25: 283-296. Rotem, J., 1988. Techniques of controlled-condition experiments. In: J. Kranz and J. Rotem (Editors), Experimental Techniques in Plant Disease Epidemiology. Springer Verlag, Berlin, Chapter 2, pp. 19-32. Seck, M. and Perrier, A., 1970. Description d'un psychrom~tre a thermocouples. Son application h la mesure des gradients d'humidit6. In: Techniques d'6tude des Facteurs Physiques de la Biosphere. INRA, Paris, pp. 223-234.
292
L. HUBER AND B. IT1ER
Shuttleworth, W.J. and Wallace, J.S., 1985. Evaporation from sparse crops - an energy combination theory. Q. J.R. Meteorol. Soc., 111: 839-855. Sutton, J.C., Gillespie, T.J. and James, T.D.W., 1988. Electronic monitoring and use of microprocessors in the field. In: J. Kranz and J. Rotem (Editors), Experimental Techniques in Plant Disease Epidemiology. Springer Verlag, Berlin, Chapter 7, pp. 99-113. Thom, A.S., 1971. Momentum absorption by vegetation. Q. J.R. Meteorol. Soc., 97:414-428. Thompson, N., 1981. The duration of leaf wetness. Meteorol. Mag., 110: 1-12. Van der Wal, A.F., 1978. Moisture as a factor in epidemiology and forecasting. In: T.T. Kozlowski (Editor), Water Deficits and Plant Growth, Vol. 5: Water and Plant Disease. Academic Press, New York, NY, pp. 253-295. Weiss, A. and Hagen, F.A., 1983. Further experiments on the measurements of leaf wetness. Agric. Meteorol., 29:207-212. Weiss, A. and Norman, J.M., 1987. Comparison of field measurements and numerical simulations of leaf wetness durations in a dry bean canopy. In: 18th Conference Agriculture and Forest Meteorology, American Meteorological Society, West Lafayette, IN, 15-18 September 1987, J4.3, pp. 52-53.