Journal of
Hydrology ELSEVIER
Journal of Hydrology ! 88- ! 89 (1997) 443-452
Soil evaporation from sparse natural vegetation estimated from Sherwood numbers Adrie F.G. Jacobs*, Anne Verhoef Department of Meteorology, Agricultural University, P.O. Box 9101, NL-6700 lib Wageningen, Netherlands
Abstract For various purposes and applications it is convenient to have a simple technique available that produces reliable estimates about the contribution of the soil sensible and latent heat of a crop canopy or natural vegetation to the total fluxes. This is especially of importance in the case of a sparse vegetation where the bare soil is the major component. Under low wind conditions a free convective state often occurs which offers an opportunity to make a simple assessment of the soil sensible heat contribution to the total sensible heat flux. In this case there exists a unique relation between the surface Rayleigh number and the surface Nusselt number. The same technique can be applied to the vapour flux by using a unique relation between the surface Rayleigh number and the surface Sherwood number, if the soil surface is wet. The last condition occurs after a rainy period. Mostly, however, the upper soil layer is dry and the soil evaporation will be limited by the surface resistance to evaporation. If the relation between soil moisture and the so-called 'soil Bowen ratio coefficient', cw, as proposed by Massman (1992) is known, a simple correction to the potential soil evaporation can be applied. During the HAPEX-Sahel experiment the above-mentioned technique has been applied to a natural vegetation under semi-arid conditions. Moreover, the modelled soil evaporation has been verified by micrc~lysimeter data. It appeared that the proposed technique is promising and is in agreement with the measurement results.
1. Introduction In a sparse canopy as well as in the situation of sparse natural vegetation, the soil contribution to the fluxes of heat and vapour can be the major component to the total convective fluxes. This is especially true in arid and semi-arid regions where the fraction * Correspondingauthor. 0022-1694/97/$17.00 © 1997- Elsevier Science B.V. All rights reserved PII S0022-1694(96)03186- I
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of bare soil is significantly higher than the plant cover (Henderson-Sellers and Gornitz, 1984). The knowledge of bare soil evaporation in semi-arid regions is also of great importance since these areas cover approximately 15% of the total land area (Heathcote, 1983) and these data are needed for climate modelling. Despite their importance for water balance as well as climate studies, very limited data about the soil contribution to the total evaporation in these regions is available (Wallace et al., 1993). Allen (1990) estimated the soil evaporation under a sparse barley crop in northern Syria and found that about 70% of the total evaporation originated from the soil. Wallace et al. (1993) measured the soil contribution to the total evapotranspiration under a millet crop in Niger and found a strong dependency on the leaf area index. Massman (1992) developed a partitioning model and applied it to his short grass steppe measurement site in northeast Colorado. He found that the soil contribution to the total evaporation was about 30%. Only a few soil evaporation models are available which produce reliable evaporation figures. Most models consist of two components, a plant component and a soil component which are represented as a plant resistance and a soil resistance. Examples are the model of Shuttleworth and Wallace (1985) and the model of Choudhurry and Monteith (1988). Recently, an interesting soil evaporation model was proposed by Massman (1992) in which the soil Bowen ratio was incorporated along with a soil evaporative resistance coefficient, the latter being connected to the moisture condition of the soil at the surface. The advantage of this type of model is that the soil evaporation is connected to simple environmental conditions which are easily measured. In the present study reported here, the eddy correlation technique along with microlysimeters were used to separate the evaporation from the soil from the transpiration from a sparse natural vegetation. The goal of the present study is to evaluate a simple evaporation model for the bare soil component under free convective conditions which often occur in semi-arid regions. Moreover, the soil resistance to evaporation as proposed by Massman (1992) has been tested and applied.
2. Theory We start from the surface energy budget, in which non-radiative fluxes are directed away from the surface, and radiative fluxes directed towards the surface positive. For a sparse canopy, the canopy energy budget at the soil is then given by (Garratt, 1992), Rn,~ = Hs + LEs + G s
(1)
where, R n.~ is the net radiative flux of the bare soil (positive daytime; negative nighttime), H.~ and LE~ the sensible and latent heat fluxes, respectively, of the soil and G~ the soil heat flux at the soil surface. Generally, it is difficult to make direct estimates of the convective fluxes, H.~ and LE.~, at the soil surface. There exists only one technique known to the authors to make a direct assessment of the latent heat flux by using micro-lysimeters. In order to make an assessment of the sensible heat flux and vapour flux at the soil surface of the canopy in an indirect way, however, various techniques are available. In the present paper we like to
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445
suggest the following procedure for free convective conditions. If in a semi-arid region the wind speed is calm, a free convection state develops at the surface. The type of convection during a certain period can easily be estimated by using the criteria (Gates, 1980; Monteith, 1981): Free convection :
Ra > 16 Re 2
Forced convection : Ra < O. 1 Re 2 Mixed convection :
(2)
16 Re 2 < Ra < 0.1 Re 2
where Ra is the Rayleigh number defined as (Kreith and Bohn, 1986): Ra =
13gbATpr ~
(3)
where, l is a horizontal characteristic length scale of the area between the major surface obstacles (Raupach, 1992), g is gravity, b is the expansion coefficient, which for a perfect gas is 1/T, where T is the absolute air temperature, AT the temperature difference between soil surface and ambient air, v the kinematic viscosity, Pr the Prandtl number defined as Pr = ~/a (for air Pr = 0.71), where a is the thermal diffusivity and Re is the Reynolds number here defined as (Jacobs et al., 1994): Re = u.s-___l/
(4)
p
where u~ is the surface wind speed measured at 0.5 m height. If these expressions are applied to the bare soil of our sparse canopy, the length scale I can be taken as the mean distance between the major surface obstacles (Raupach, 1992), the bushes, which at the experimental site was 6.5 m. In our case (see later) it appeared that most conditions agreed with the free or mixed convection state. Then the exchange of sensible heat as well as the soil evaporation is dominated by the free convection exchange mechanism. The dimensionless heat transfer can be expressed in the Nusselt number, Nu, defined as (Kreith and Bohn, 1986): H~.l Nu
-
(5)
X.AT
where X is the thermal conductivity of still air (X = 0.0257 W m -~ K-I). For a flat and horizontal surface, if Ra > 107, the Nusselt number equals the relation (Jakob, 1950): 1
Nu=O. 14 Ra -3
(6)
Finally by combining Eqs. (5) and (6), for the sensible heat flux at the soil surface, Hs, is found: 1
H~ = O. 1l XR a 3 A T
(7)
which also means (Kreith and Bohn, 1986) that during a free convective state the sensible heat transport is independent of the horizontal length scale l, since R a i l 3.
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In analogy to the sensible heat transport the mass transport under wet soil conditions can be estimated by using the Sherwood number, Sh, which is defined as (Kreith and Bohn, 1986): 1
Sh= pD(x2_xl)=Nu Es'l (Sc)
1
=0.14 Ra
½(~rr) ~
(8)
where, Es is the mass flux of vapour per unit surface area from the wet surface, P is density of air, x is the water vapour mixing ratio, D is the molecular diffusivity of water vapour in air and Sc is the Schmidt number defined as Sc = riD, (for air, Sc = 0.63). If the surface soil is wet the vapour flux equals the potential soil evaporation: Es, pot=
#ShD(x2 - xl ) l
(9a)
or
1
(Sc)pNu ~r 3D(x2-xl) Es, pot=
1
(9b)
which means also that during the free convection period the soil vapour transport is independent of the length scale I. c rg0 8(defined ) Tj32.64 At the soil surface, the soil surface Bowen ratio,/~s, can be defined accord (Sc)00 Tw3convec 1 70.56 365.5
A.F.G. Jacobs, A. Verhoef/Journal of Hydrology 188-189 (1997) 443-452
447
3. Materials and methods During the late summer period at the end of the wet season of 1992 the intensive measurement period of the HAPEX-Sahel climatological field experiment took place in Niger, West Africa. The main goal of this experiment was to obtain data which can serve as input parameters in global circulation models (Goutorbe et al., 1994). The Department of Meteorology of the Agricultural University of Wageningen, being a contributor to this measurement campaign, carried out experiments at the 'West-Central supersite', about 50 km west of the capital Niamey (13°32'60"N, 2°30'68"E). Here, soil, plant and meteorological data were gathered on a fallow savanna site. The fallow savanna consisted of a sublayer of grasses (e.g. Digitaria gayana, Ctenium elegans, Eragrostis pilosa and E. tremula) and some herbs (e.g. Mitracarpus scaber, Indigofera and Jacquemontia tamnifolia), and scattered Guiera bushes with a height of about 2 m and a mean spacing between the bushes of about 6.5 m. Because of the late start of the rainy season (end of June) the undergrowth stayed rather sparse and low (maximum height 0.5 m), resulting in a bare soil percentage of 30%. The soil was classified as a loamy sand with clay contents of approximately 5%. Values for the dry bulk density, were 1600, 1580, 1480 and 1400 kg m -3 for the depths of 0.05, 0.10, 0.25 and 0.45 m, respectively. These large values are a result of high sand contents and a high soil compaction possibly caused by the excrements of termites. Above the vegetation, mean wind speed, mean dry and wet bulb temperature profiles were measured of which the lowest level, used in the present study, was 0.5 m above the ground. The eddy correlation technique was used to estimate the total fluxes of momentum, heat, water vapour and CO2 by installing a sonic anemometer (Solent type AI012R) and a H20/CO2 sensor (LICOR type LI-6262) at a height of 5 m (Heusinkveld et al., 1994). The incoming and reflected short wave radiation (Kipp solarimeters) and net radiation (Funk net radiometer of Middleton) were measured at a height of about 10 m above the soil. Soil temperatures were measured at five depths, by horizontally inserted Pt-100 probes at depths of 0.03, 0.05, 0.10, 0.25 and 0.50 m, the soil heat flux was estimated using the calometric method (Verhoef et al., 1995). To obtain reliable assessments of the soil surface temperature, a pyrometer (Heiman type KT-15) was installed at a height of 1.6 m, directed at the soil surface. This pyrometer has an 8° field-of-view, which means that at an observing height of 1.6 m, the viewed soil surface was about 0.016 m E. During the rainy and drying period, soil moisture content was measured every second day at four depths (0.05, 0.10, 0.25 and 0.45 m) in order to estimate the soil moisture content profile. The soil moisture contents were obtained by the TDR-method (FOM/m, Easy test Ltd, Poland). The TDR-probes were inserted vertically to obtain spatially averaged moisture values. Saturated soil moisture content was 0.36 m 3 m -3. However, the highest recorded volumetric moisture values during the campaign were 0.15 m s m -3 as a result of the high drainage capacity of the soil, which caused the soil to dry before reading of the TDRequipment. Precipitation data were obtained via the EPSAT-Niger (Lebel et al., 1992) rain gauge station system which had one rain gauge installed within a few hundred metres of the field site. Soil evaporation was estimated using six micro-lysimeters of the type described by
448
A.F.G. Jacobs, A. Verhoef/Journal of Hydrology 188-189 (1997) 443-452
Boast and Robertson (1982). Three lysimeters were installed in sunlit locations and three lysimeters were installed in the shade under a Guiera bush. During the selected period the micro-lysimeters were weighed in the field on a precision balance (Mettler) about every 2 h during daytime. To avoid errors due to isolating the bottom of the soil samples within the micro-lysimeters from the underlying soil, new samples were taken every day. More details about instrumentation and data processing can be found elsewhere (Heusinkveld et al., 1994; Verhoef et al., 1995; Lloyd et al., 1996). 4. Results and discussion
Four successive days and nights with different weather conditions at the end of the rain period were selected for analysis. Throughout the whole period, time averaged measurements as well as eddy correlation measurements were taken. There was one exception at DOY 251 when no turbulence measurements were taken due to heavy thunderstorms. In Fig. l the main characteristics of the weather during the selected period have been plotted to give a general impression. The upper 5-cm soil layer was somewhat dried out during the first selected day, however, due to the heavy rains around midnight of DOY 250/251 the soil moisture increased considerably. In Fig. 2 the surface Rayleigh number (Eq. (3)) has been plotted versus the square of the surface Reynolds number (Eq. (4)). The criterion for forced convection, Ra > O. 1 Re 2, has been depicted as well. It clearly can be inferred that the majority of the conditions can be recognized as free or mixed convection. Only four half-hour intervals of the total of 192 intervals can be found which fulfilled the forced convection criterion. These periods occurred during the thunderstorms around the midnight of DOY 250/251. 10
NIGER 1992; DOY: 250 - 253
[~ ,-~
~'
"-"-
',,
:
i
',
,~
:" ;
!
i:
E
..
X
A
-6 .~
p~
Ix.
~25
~ 20 15
-3
II
10
II hi
5
"v
0
l. u u m l m a l a u m m a
0
6
"--", 1|4 ~
un~nmmR~a~n~m.a
12 18 24 6
IWlndS~edlO~)l -"
Im
-2
I I _.." "-..'-'-
v
mm ~u~n~'m~w~l~'m
12 18 24 6
mmm
a'ml~a~
......
12 18 24 6
".,;~'
aml~mmmm~l~
12 18
Fig. 1. General weather conditions during the 4 selected days. The preceding period was dry and hot. The last previous rain events occurred on DOY 243 (60 mm) and DOY 244 (0.5 mm).
A.F.G. Jacobs, A. Verhoef/Journal of Hydrology 188-189 (1997) 443-452
1~1=
•
•
449
J
al~, •,L
10- X J NL •
•
NIGER 1992; DOY: 250- 253
•
0
0
1000
~ 2 (-r'rnes10E9) Fig. 2. The surface Rayleigh number versus the surface Reynolds number. The horizontal length scale I was taken as the mean distance between bushes (I = 6.5 m). In the surface Reynolds number the mean horizontal windspeed at z = 0.6 m was used.
The evaporation process is a process which is dominated by the amount of available energy, i.e. the net radiation. Therefore in Fig. 3 the course of the net radiation has been plotted for the selected period. Moreover, the total latent heat (sum sparse vegetation and soil contribution) measured by the eddy correlation technique has been 700
Niger 1992; DOY: 250 - 253 600 Total t.,am~ Heat
~Pot, LaL Heat Soil
50O
.~aoo
~ 200 100
-100
0
6
12 18 24
6
12
18 24
6
12 18 24
6
12 18
Time (9mt) Fig. 3. The course of the net radiation, the total measured latent heat flux (vegetation plus soil contribution) and the potential soil evaporation (Eq. (12) with cw = 1).
450
A.F.G. Jacobs, A. VerhoeflJournal of Hydrology 188-189 (1997) 443-452 10
8-
-29 e~a) MGER: 1
6-
4-
2-
0
0.05 011 SOil Moleture (m3/m3)
0.15
Fi 8. 4. The relation between the top soil moisture content and the soil Bowen ratio coefficient, cw.
given. Also in Fig. 3, the calculated potential soil latent heat flux has been depicted (Eq. (12) with Cw = 1). In Fig. 4, the soil Bowen ratio coefficient, Cw, has been depicted versus the soil moisture of the upper soil layer. Here, the measured soil moisture data between 0 - 0 . 0 5 m depth and the lysimeter data were used for the period preceding the selected days. The soil Bowen 2
10
N~
18ff2 DOY 251: Cw = 1.0
DOY 250. Cw = 6.5
DOY 252: Cw = 1.2
y
i, w.
-6
E
.5
§
O.
-2
0
6
12
18
24
6
12 18 time (gmt)
24
6
12
18
,,, 0
24
Fig. 5. The course of the cumulative calculated evaporation rates (cw = variable) and the measured results from the sunlit and shaded iysimeters.
A.F.G. Jacobs, A. Verhoef/Journal of Hydrology 188-189 (1997) 443-452
451
ratio coefficient was taken as the ratio between the daily lysimeter results (actual soil evaporation) and the daily potential soil evaporation calculated using Eq. (9) (potential soil evaporation). In addition, an exponential curve fit has been plotted. From the result of Fig. 4 it can be seen that at high moisture content the cw value is more or less constant around the numerical value cw = 1. At moisture content lower than 0.10 m 3 m -3, the c~ coefficient increases rapidly at a more or less exponential rate. In Fig. 5, the calculated as well as measured cumulative soil evaporation results have been plotted. The calculated evaporation figures were obtained by using a daily variable soil Bowen ratio coefficient, cw, dependent on the soil moisture content of the upper soil layer. From this result it can be concluded that the proposed technique to estimate the contribution of soil evaporation to the total evaporation can be used adequately if soil moisture data are available and, in addition, the soil Bowen ratio coefficient, c , , is known.
5. Conclusions From the foregoing the following main conclusions can be drawn: 1. If the soil exchange processes of heat and vapour are in the free or mixed convection state, the sensible heat contribution and the soil evaporation contribution to the total fluxes of sensible and latent heat, respectively, can be estimated by using Nusselt and Sherwood numbers for free convection. 2. By using the Sherwood number to estimate the actual soil evaporation, the dependency of the soil Bowen ratio coefficient, cw, as function of the soil moisture content of the upper soil layer must be known. This relation for a particular soil can be obtained by using micro-lysimeters. 3. From the limited micro-lysimeter data available
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A.F.G. Jacobs, A. Verhoef/Journal of Hydrology 188-189 (1997) 443-452
Boast, C.W. and Robertson, T.M., 1982. A "'micro-lysimeter" method for determining evaporation from bare soil: description and laboratory evaluation. Soil Sci. Soc. Am. J., 46: 689-696. Choudhurry, B.J. and Monteith, J.L., 1988. A four-layer model for the heat budget of homogeneous land surface. Q.J.R. Met. Soc., 112: 373-398. Garratt, J.R., 1992. The Atmospheric Boundary Layer. Cambridge Atmospheric and Space Sci. Series, 316 pp. Gates, D.M., 1980. Biophysical Ecology. Springer-Verlag, New York, 61 i pp. Goutorbe, J.-P., Lebel., T., Tinga, A., Bessemoulin, P., Brouwer, J., Dolman, A.J., Engman, E.T., Gash, J.H.C., Hoepffner, M., Kabat, P., Kerr, Y.H., Monteny, B., Prince, S., Said, F., Sellers, P. and Wallace, J.S., 1994. HAPEX-SaheI: a large scale study of land atmosphere interactions in the semi-arid tropics. Ann. Geophys., 12: 53-64. Heathcote, A., 1983. The Arid Lands. Longman, London. Heusinkveld, B.G., de Bruin, H.A.R., Verhoef, A., Antonysen, F. and Hillen, W.C.A.M., 1994. Procedures for reliable eddy covariance measurements of atmospheric heat and CO2-fluxes. In: WMO, Instruments and observing methods. TECEMO, Report No. 57. Jacobs, A.F.G., Van Boxel, J.H. and EI-Kilani, R.M.M., 1994. Nighttime free convection characteristics within a plant canopy. Bound.-Layer Meteorol., 62: 375-387. Jakob, M., 1950. Heat Transfer. John Wiley and Sons, New York, 758 pp. Kreith, F. and Bohn, M.S., 1986. Principles of Heat Transfer. Harper and Row Publishers, New York, 700 pp. Lebel, T., Sauvageot, H., Hoepffner, M., Desbois, M., Guillot, B. and Hubert, P., 1992. Rainfall estimation in the Sahel: the EPSAT-NIGER experiment. J. Hydrol. Sci., 37: 201-215. Lloyd, C.R., Bessemoulin, P., de Bruin, H., Cropley, F., Culf, A.D., Dolman, A.J., Elbers, J., Moncrieff, J., Monteny, B. and Verhoef, A., 1996. A comparison of surface flux measurements during HAPEX-Sahel. J. Hydrol., this issue. Massman, W.J., 1992. A surface energy balance method for partitioning evapotranspiration data into plant and soil components for a surface with partial canopy cover. Water Resources Res., 28: 1723-1732. Monteith, J.L., 1981. Evaporation and the environment. Symp. Soc. Exp. Biol., 19: 205-234. Raupach, M.R., 1992. Drag and drag partition on rough surfaces. Bound.-Layer Meteorol., 60: 375-395. Shuttleworth, W.J. and Wallace, J.S., 1985. Evaporation from sparse crop - an energy combination theory. Q.J.R. Met. Soc., II1: 839-855. Verhoef, A., Van den Hurk, B.J.M., Jacobs, A.F.G. and Heusinkveld, B.G., 1995. Thermal soil properties for vineyard (EFEDA-I) and savanna (HAPEX-Sahel) sites. Agric. For. Meteorol., submitted. Wallace, J.S., Lloyd, C.R. and Sivakumar, M.V.K., 1993. Measurement of soil, plant and total evaporation from millet in Niger. Agric. For. Meteorol., 63: 149-169. Henderson-Sellers, A. and Gornitz, V., 1984. Possible climate impacts of land cover transformations, with particular emphasis on tropical deforestation. Clim. Change, 6:231-258.
