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Thermal soil properties for vineyard (EFEDA-I) and savanna (HAPEX-Sahel) sites
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AGRICULTURAL AND FOREST METEOROLOGY Agricultural and Forest Meteorology 78 (1996) 1-18
Thermal soil properties for vineyard (EFEDA-I) and savanna (HAPEX-Sahel)sites Anne Verhoef *, Bart J.J.M. van den Hurk, Adrie F.G. Jacobs; Bert G. Heusinkveld • Department of Meteorology, Wageningen Agricultural University, Duivendaal 2, 6701 AP Wageningen, The Netherlands
Received 30 March 1995; accepted 21 April 1995
Abstract
This paper describes the course of topsoil thermal conductivity, A, diffusivity, at, and heat capacity, C h, during two measurement campaigns, conducted in semi-arid areas--the EFEDA-I experiment and HAPEX-Sahel. For the derivation of a , five methods (the Amplitude, Phase, Arctangent, Logarithmic and Harmonic equation) were compared. Values of C h were derived from measurements of soil moisture content, 8, and dry bulk density. A was either measured directly (the non-stationary probe method) or calculated from A = a . C h. Thermal soil properties were clearly related to 0 (and thus rainfall) throughout the measurement campaigns: hardly any changes occurred during the EFEDA-I experiment where continuous dry conditions prevailed, whereas for HAPEX-Sahel a clear decrease in all thermal properties was observed after the last rainfall. For calculation of ct, the Amplitude and the Harmonic equation gave the best results. Calculation of at and A beneath the vegetation plots yielded unreliable results, mainly due to shading effects causing more than one temperature maximum. : Direct measurement of A yielded unrealistically low values for the dry soil conditions as encountered in Spain, due to poor contact between.probe and s o i l A correction for the contact resistance is necessary to obtain better estimates. For HAPEX-Sahel, measured and calculated A values were much closer, mainly for reasons of higher 0 values and a high soil compaction which ensured better contact between soil and probes.
* Corresponding author at: Institute of Hydrology, Crowmarsh Gifford, Wallingford, Oxon OX10 8BB, UK. 0168-1923/96/$15.00 © 1996 Elsevier Science B.V. All fights reserved SSDI 0 1 6 8 - 1 9 2 3 ( 9 5 ) 0 2 2 5 4 - 6
2
A. Verhoefet al./Agricultural and Forest Meteorology 78 (1996) 1-18
I. Introduction
If advection and storage are neglected, the soil heat flux density, G, is one of the four components of the surface energy balance:
R.=~+LE+~
(1)
where R , is the net radiation, H is the sensible heat flux, and LE is the latent heat flux caused by vaporization (all fluxes are in W m - Z ) . In the case of a closed, well-watered canopy the soil heat flux is usually relatively small and parameterized as a fraction of R n (0.1-0.2, depending on the type of crop and soil moisture content). For sparse canopies under semi-arid or arid conditions, however, G can account for a large part of the energy balance (up to 40% of R n) and being equal to or even higher than LE. Under these circumstances accurate estimates of G should be obtained. G is determined by the thermal soil properties (thermal conductivity, A, heat capacity, C h, and apparent thermal diffusivity, a ) which are in turn dependent on soil moisture content, 0, soil composition and vegetation cover (shading, root influence on 0). These thermal soil properties vary in space causing heterogeneity and in time. Although heterogeneity plays a role for closed canopies in temperate climates, its influence on G is much larger for sparse canopies. Two types of heterogeneity can be distinguished which are important for micrometeorological investigations. First, meso-scale heterogeneity can be induced by spatially variable rainfall which influences A, C h and a (and thus G) through changes in moisture content on a scale of several kilometres. The second type is heterogeneity on the micro-scale, which is especially important for sparse canopies. This arises because the total soil surface is composed of soil under the open (bare, or slightly vegetated) patches in between the isolated plants/bushes and soil located under the canopy. The vegetation will influence the underlying soil in two ways; it will shade it and it will influence 0, and thus thermal soil properties and soil heat flux. Besides spatial variation, a large temporal variation is expected if heavy rainfall is alternated by severe droughts. The recently conducted EFEDA-I and HAPEX-Sahel experiments provided an excellent opportunity to study the spatial (meso-scale and micro-scale) and temporal variability of the thermal properties and G for sparsely vegetated areas. This paper describes the thermal properties of two soils (located in a vineyard and a savanna, respectively) which were sampled during the above-mentioned experiments. An appraisal is made of the changes during the growing season (temporal variability), resulting from soil drying. The impact of changing moisture conditions and effects of shading on thermal soil properties on the spatial micro-scale (below and in between canopy elements) is also investigated. The values of A, o~ and C h, derived here, can be used as input in SVATs or GCMs.
A. Verhoef et al. /Agricultural and Forest Meteorology 78 (1996) 1-18
3
2. Materials and methods
2.1. Site description and soil characteristics 2.1.1. EFEDA-I, vineyard The EFEDA-I experiment was conducted in Tomelloso (Spain, latitude 2°55'48" N, longitude 39008'30 " E) during June 1991 (Bolle et al,, 1993). The soil measurements were collected at the Wageningen Agricultural University Meteorological site, which was located in a sparsely vegetated vineyard (Vitis Vinifera L. cv. variety: Airen), with row-spacings of 2.5 m and between-plant spacings of about 2.0 m. The topsoil consisted of a reddish sandy loam, sparsely covered with stones with a maximum diameter of 3 cm. The layer from 25-35 cm was a silt loam, whereas the other layers were sandy loams (Droogers et al., 1993). In June, the upper soil layers were already dry. The last rainfall (0.5 mm) occurred on June 4 (day 155). In the preceding week about 30 mm of precipitation was recorded (Sene, 1994). Soil temperatures were sampled with PT-100 resistance probes, which were developed at the Department of Meteorology, Wageningen. Soil temperatures below the between-row bare soil surface were measured at 5 depths: 0.03, 0.05, 0.10, 0.25 and 0.50 m. To measure the soil temperatures below the canopy, 5 resistance thermometers were inserted at the same depths north of a vineplant at a distance of 0.3 m from the trunk. The soil moisture content, 0, was measured by TDR sensors at depths of 0.10, 0.20, 0.30, 0.40 and 0.50 m, where the dry bulk density, Pd, was found to be 1340, 1200, 1240, 1210 and 1190 k g m -3 (Droogers et al., 1993). At 0.10 m depth 0 varied from 0.08 to 0.06 m 3 m -3 during the measurement campaign. For deeper layers values of up to 0.18 were recorded with little variation during the season (Fig. l(a)). So-called non-steady-state probes (Van Loon, 1991), developed at the Department of Meteorology, Wageningen, were used to measure thermal conductivity. Two thermal conductivity profiles were sampled twice a day. One was located in the vicinity of a plant with probes at depths of 0.03, 0.05, 0.10, and 0.20 m. The probes located between two rows were installed at depths of 0.03, 0.12, 0.22, and 0.35 m.
0.25
FOAgvnyr=: (a)
o~
........
~E ~, o.1s
~
o 150
Fig.
]. Soil
Hapcx-Sahc]
os HAPEXSh 9 vinn II
-- " " - - -o.3om
~-:":'::-'-'~-"~'-~:-'~::-~=':.:::'.~
i
r
i
t
J
15S
160
165 Day number
170
175
moisture campaign
content, (b).
0, at several
(b)
~ ~l=
o~
~
0.15
o 180
depths during t h e
--O.06m ~ -o.lOm
.... ~ .... . . . . . 0.40-0.50 rn ~
- - 230
EFEDA-I
/...,
.
i
i
i
i
240
250
260 Oar/ number
270
measurement
280
290
campaign (a) and during
A. Verhoefet al./Agricultural and Forest Meteorology 78 (1996) 1-18
4
HAPEX-Sahel 1992, 70
savanna
JllllEIIIILIIIIILIIlillllllPkLIllli[llllllllllllliklllllliillllllBIIllLIIL
60 50 E E
40
~
30 20
10
Day number
Fig. 2. Precipitation during the HAPEX-Sahelmeasurementcampaign. For the assessment of a , continuous measurements of soil temperatures were needed which were only available for the days of June 5, 6, 9, 12, 17, 20, 24, 25, 26 and 29. For the other days values were interpolated. 2.1.2. HAPEX-Sahel, savanna
The HAPEX-Sahel experiment (Goutorbe et al., 1994) took place in Niger from August until October 1992. Results are presented for the so-called Central West Site, 50 km east of Niamey (latitude 13°32'60" N, longitude 2o30'68" E). The savanna consisted of scattered shrubs (Guiera senegalensis) with an undergrowth of several species of grasses and herbs. Because of the late start of the rainy season (end of June) the understorey remained rather sparse and low (maximum height 0.5 m). The soil was classified as a loamy sand (Soet et al., 1993). The ~d was measured as 1600, 1580, 1480 and 1400 k g m -3 for the depths of 0.05, 0.10, 0.25 and 0.45 m, respectively (Soet et al., 1993). The larger Pa values, compared to the EFEDA-I experiment, are a result of higher sand contents and a higher soil compaction possibly caused by the excrements of termites. As a result of frequent rainfall (Fig. 2) temporal variability of soil moisture was large, compared to EFEDA, with 0 varying from 0.16 m 3 m -3 after a rainstorm to 0.03 m 3 m -3 during a drying period (Fig. l(b)). Soil temperatures were measured with horizontally inserted PT-100 resistance thermometers at two plots in close proximity. One of the plots was hardly vegetated ('bare' plot) whereas the other plot exhibited
A. Verhoef et aL / Agricultural and Forest Meteorology 78 (1996) 1-18
5
more vegetation (grass and herbs) than average. Each temperature array consisted of 5 thermometers installed at depths of 0.03, 0.05, 0.10, 0.25, and 0.50 m. The A probes were placed in between the temperature sensors, at depths of 0.015, 0.04, 0.075, and 0.15 m. For reading, they were connected to a portable datalogger several times per day (3 times during the wet period, 1 or 2 times during the drying period).
2.2. Theory of thermal soil properties Surface soil heat fluxes can be estimated with several methods of which the most commonly used are the Calorimetric, Gradient, Harmonic and Plate method (Tanner, 1963; Kimball and Jackson, 1975; Ten Berge, 1990), All methods require the installation of at least 1 thermometer (Plate method, Harmonic method) or more (2 for the Gradient method and several, at least 4 or 5, for the Calorimetric method). The Plate method uses thermopile flux plates. Furthermore, it demands an estimate of heat storage of the soil layer above the sensor. Besides measurements of temperature or the flux at a certain depth, an estimate of the soil thermal properties (A, a and C h) is needed. The Calorimetric method requires estimates of C h, whereas for the Gradient and the Plate method values of A and C h (calculation of storage) are required. For the Harmonic method all thermal properties are used. Besides careful installation and depth location of the sensors and minimum disturbance of the soil, much attention has therefore to be paid to the determination of the thermal soil properties.
2.2.1. Volumetric heat capacity The volumetric heat capacity, C h, is defined as the change of heat content per soil volume and per change of temperature (J m - 3 K - ~). It can be calculated if values for bulk density and moisture content for the soil layer under consideration, using C h = ECh,i~)i
(2)
i
where Ch, i is the volumetric heat capacity for each soil component and q~; is the volume fraction of component i. Organic matter and air were not taken into account because their contribution is neglible. The volumetric heat capacities for the mineral soil components, C,,s, and water, Ch., are 2.0, and 4.2 MJm -3 K - i , respectively (Ten Berge, 1990). With knowledge of the water and solid phase fractions, C h for the upper soil layer can be calculated using b
Ch = C h , s Pd - - + Ch,lO Ps
(3)
where Ps is the density of the solid phase (kgm -3) and ~9d the dry bulk density (kg m - 3). Ps was taken as 2650 kg m - 3.
6
A. Verhoefet al./Agricultural and Forest Meteorology 78 (1996) 1-18
2.2.2. Thermal diffusivity The soil thermal diffusivity, a (m 2 s-1), is the ratio of thermal conductivity to the volumetric heat capacity: c~ = A / C h
(4)
Horton et al. (1983) evaluated 6 methods for determining ct. For the calculation of ct for the two data-sets five of their methods will be applied, viz. the Amplitude equation, the Phase equation, the Arctangent equation, the Logarithmic equation and the Harmonic equation. The equation describing the conductive heat transfer in a one-dimensional isotropic medium is given by
6T - -
6t
82T -
(5)
6z 2
In this case a is independent of depth and time. Using the Fourier series representation, soil temperature near the soil surface can be described by a sum of sine and cosine terms according to the following equation M
T ( t ) = T + E [ A,cos(no~t) + Bnsin(noJt)]
(6)
n=l
where the overbar denotes an average in the time interval considered, M is the number of harmonics and A n and B n are the amplitudes, o~ is the radial frequency ( = 27r/P), with P representing the period of the fundamental cycle. The following formulas base their calculation of a on simplifications (analytical solutions) of Eq. 5 applying Eq. 6 (with different values for M) to describe the temperature.
2.2.2,1. Method 1. The Amplitude equation. The amplitude equation is given by
=2
[z2z]2 In AT?-A2
(7)
where A 1 and A 2 a r e the amplitudes at depths z~ and z2, respectively. Determination of a from this equation requires measurement of the maximum and minimum temperature at both depths during the period of the fundamental cycle (in our case 24 h).
2.2.2.2. Method 2. The Phase equation. The Phase equation is given by a=
1 [z2-zj] 2 2---~[ 6t l
(8)
in which 6 t ( = t 2 - t 1) signifies the time interval between the measured occurrences of maximum soil temperature at depths zl and z2-
A. Verhoef et al. / Agricultural and Forest Meteorology 78 (1996) 1-18
7
2.2.2.3. Method 3. The Arctangent equation. With M = 2, the apparent thermal diffusivity can be calculated from
o,( z2 - z,)2 2 arctan (T,
r3)(r;
(9) T,)(T;
T/~)
where temperatures T~ and T" are recorded every 6 h (subscripts 1 to 4) at two depths, z~ and z2 (denoted by '), respectively.
2.2.2.4. Method 4. The Logarithmic equation. It was shown by Seemann (1979) that, in analogy to Method 3, the apparent thermal diffusivity can also be calculated from a=
[
0.0121(z2 - z,)
(10)
In (T1- T3)2 "~-(T2S T4)2
2.2.2.5. Method 5. The Harmonic equation. The analytical solution of Eq. 5 according to van Wijk (1963) is
M T(z,t)=T+
~ (Co,e-Z~-L-7~sin(ntot+qbo,-Z~))
n=l
(11)
where Con and ~b0n are the amplitude and phase angle of the n th harmonic for the upper boundary, respectively (Horton et al., 1983). The harmonic analysis of temperatures at zi will yield M values of Con and ~bon which can give an estimate of temperature at z2 (provided the soil is homogeneous in the vertical) with the help of Eq. 11, if a proper value of a is given. ot can be found by selecting an a (through iteration) which gives the smallest sum of squared differences between the measured and estimated temperature at z2. The sum of squares will be composed of 24 whole (0,1,2 . . . . . 24) or half-hour (0.5,1.5 . . . . . 23.5) differences between measured and calculated temperature.
2.2.3. Thermal conductivity Thermal conductivity, A (W m - ~ K - ~), was measured directly using non-steady-state probes (Van Loon, 1991). Furthermore, it was calculated by Eq. 4.
3. Results 3.1. Soil heat capacity 3.1.1. EFEDA-I, vineyard Fig. 3(a) gives the variation of C h at 5 depths. After the last rainfall, maximum values of around 1.6 M J m -3 K - 1 w e r e reached at depths of 0.30 and 0.50 m. The
8
A. Verhoefet al./Agricultural and ForestMeteorology 78 (1996) 1-18 EFEDA 1991,
vineyard
HAPEX-Sahel 2
(a)
i I (b)
,
1992, ,
savanna ,
, I- -
, OXO-O,OS m
I
1.8
1.8 ~
?"
1.6
~
-
~6
t ~,
p.......... .....
~.
.~.
r~
~ ;":':~'~' ..
o.10-o,25 m
........ o
"~" "Z'" " ~,.- ..:. ~::.:.,......
25-o,5o m
12
1 S0
155
160
165
170
Day n u m b e r
175
180
230
240
250
~60
2 ]0
280
290
Day number
Fig. 3. Heat capacity as calculated with Eq. 2 for the EFEDA-I measurement campaign (a) and for the HAPEX-Sahel experiment (b). minimum value was about 1.1 M J m -3 K -1. After day 160, C h remains more or less constant for all soil layers, which is caused by the small changes in 0. Soil layering may cause C h to change abruptly with depth. 3.1.2. HAPEX-Sahel, savanna
The variation of heat capacity during the campaign is shown in Fig. 3(b) for 4 depths. During the rainy period maximum values of 1.7 M J m -3 K -1 were attained. The minimum value was about 1.2 MJ m -3 K - t for the upper depth, occurring 3 weeks after the last rainstorm. Both experiments show a comparable range of C h values. Nevertheless, the values in the upper soil layers for the HAPEX-Sahel experiment during the first half of the campaign were considerably higher than those during the EFEDA-I experiment as a result of wet soil conditions. This led to a large temporal variability for the HAPEX-Sahel experiment. 3.2. Soil diffusivity
Thermal diffusivity was only calculated for the top 10 cm of soil (from the harmonic analysis of temperature at 0.03 m depth, the a values at 0.05 and 0.10 m were derived). The reason for this is that attempts to calculate a for 0.25 and 0.50 m (with the Harmonic equation which, according to Horton et al. (1983), is the most reliable method to calculate or) yielded unrealistic values, which implies that the soil was probably not homogeneous in the vertical direction. However, for calculation of G we only need a value for a at the upper few centimetres of soil, and we can possibly assume the first 10 cm of the soil to be uniform. 3.2.1. EFEDA-I, vineyard
The thermal diffusivity of the between-row soil at 0.05 m depth is given in Fig. 4(a) (temperatures at half-hour intervals of time were used). The Phase equation is not shown: it appeared that this method calculated a constant ct during the entire period
A. Verhoef et al. / Agricultural and Forest Meteorology 78 (1996) 1-18 EFEDA
1991,
HAPEX-Sahel
vineyard 2
1992,
9
savanna
(hi i
%
"
i
H a t r n o m ¢ n~lhod
- --
- ~'et=ng~mt
-
-- - Lt~arlthtr~
l .-...- I
m~hod method
~_ os
~_ o.s
0 1 SO
[
i
i
155
160
~6 5
Day
number
_
i
i
170
175
0 180
l
230
240
-
-
[
~
L
-
-
250
.
260
Day
l
270
_
[
280
-
-
[
number
Fig. 4. Course of thermal diffusivity, according to several methods, during the EFEDA-I measurement campaign (a) and during the HAPEX-Sahel measurement campaign (b).
because the 1-hour resolution of temperatures resulted in the same value of ~ t (see Eq. 8) for all days. All methods show a similar course: after the last occurrence of rain (day 154), a decreases rapidly to a more-or-less constant value. Some dewfall on day 168 and 169 appears to influence soil moisture content (and thus a ) to some extent. The sudden increase after day 177 is caused by artificial wetting of the soil temperature plot, which was done to obtain a larger range of 0 values for derivation of the thermal soil properties. The Amplitude, Logarithmic and Harmonic equation calculate low, but mutually consistent, a values during the dry period ( ~ 0.25 mm 2 s - 1). The Arctangent method is approximately 2 times higher. The Harmonic method exhibits relatively high a values (between day 171-176), which cannot be related with increased moisture content. For these days (not shown) the summed difference between the measured and fitted temperature at 0.05 m is large (the fitted temperature consistently overestimating the daytime measured temperature). This large difference between observed and fitted temperature was always accompanied with high soil temperatures. This same, relatively large, discrepancy between fitted and observed temperatures for hot, relatively dry soils has been observed for the HAPEX-Sahel experiment. Four explanations for this can be suggested. • After rainfall, part of the soil heat flux is being used for soil evaporation. This would make the temperatures at 0.05 m cooler than expected from Fourier analysis of the temperatures at 0.03 m (if the evaporation front lies between 0.03 and 0.05 m). If the PT-100 at 0.05 m is in fact placed at a deeper depth this fact is obscured by the evaporation. A change in soil composition or density occurs below 0.03 m. • The occurrence of a change of a during the day; because of diurnal fluctuation in 0, a is expected to be higher during the morning and lower during the afternoon. The assumed validity of sinusoidal variation. Shading of the soil by the vines (thus causing two temperature maxima) led to anomalous within-row values of a. These values are therefore not presented here.
1o
A. Verhoef et al. / Agricultural and Forest Meteorology 78 (1996) 1-18
HAPEX-Sahel
~
1992, s a v a n n a
I
1
I
I
I
I
I
I
I
I
I
I
0.02
0.04
0.06
0.08
0.1
0.12
1.5
E >
0.5
0
0
0.14
Soil moisture content (m3m"3)
Fig. 5. Relationship between soil moisture content and calculated (Harmonic method) diffusivity for the HAPEX-Sahel experiment. 3.2.2. HAPEX-Sahel, savanna
Fig. 4(b) gives the a values during the campaign obtained from Method 1, 3, and 4 using hourly mean values for soil temperature. During the rainy period, a reaches maximum values of around 1.5 mm 2 s -~ . This value is high but not unusual for wet sandy soils. It agrees with the high A values found for this soil at relatively low 0 values (See Section 3.3.2). A few days without rainfall (e.g. between day 244 and 250) led to a considerable decrease of ct. This is caused by the high evaporative demand of this region, which lowered 0 rapidly. After the beginning of the dry season, a rapidly declines to values around 0.3 mm 2 s -1. To investigate the dependence of a on the choice of the temperature value used, the diffusivity was also calculated with 24 half hourly mean values as input (not shown). It appeared that the Amplitude method is most influenced by this change, having a more irregular character, indicating that the maximum a n d / o r minimum temperatures are probably lying closer to the whole hours than to the half-hours. The Logarithmic equation, although giving a temporal variation similar to the other methods, was much higher and is therefore not shown in these graphs. If a is plotted against moisture content at 0.05 m a clear linear relationship is found (Fig. 5, r E = 0.80). This supports the validity of our calculations. For the EFEDA-I dataset there was insufficient variation in 0 to show a relationship between 0 and ct. Temperature profiles were also measured underneath a more vegetated soil plot. Attempts to calculate a for this location led to erratic and illogical results for all methods. This was caused by the irregular temperature profiles (caused by
A. Verhoef et al./Agricultural and Forest Meteorology 78 (1996) 1-18
11
the vegetation) and by the fact that the actual depth at which the sensors were located deviated considerably from the intended installation depth. This discrepancy might have been the result of soil movement caused by severe flooding during several rainstorms. 3.3. Soil thermal conductivity 3.3.1. E F E D A - L vineyard 3.3.1.1. Measured thermal conductivity. The directly measured values of A at 4 depths
are given in Fig. 6(a) (between-row) and (b) (within-row) for the entire measurement campaign. It appears that within-row h values are slightly higher than the values for the between-row soil, possibly shading reduces soil evaporation. Furthermore, the curves reflect that after day 155 the soil moisture content soon reached an equilibrium value (cf. Fig. l(a)). The large differences in observed A between days 154 and 155 may be the result of the last rainstorm on day 153. On these days, the between-row h value is higher than the within-row h value, probably as a result of the sheltering effect of the vineplants. Vertical and horizontal redistribution of soil moisture and reduced evaporation rates from the soil in the vicinity of the plants result in the between-row A value being lower than the within-row h value for the rest of the campaign. The values for the within-row A sensor at a depth of 0.20 m were clearly deviating (even taking into account the higher 0 values) from those for the other probes and are therefore not shown in Fig. 6(b). 3.3.1.2. Calculated thermal conductivity. Values of A were also derived from Eq. 4,
where C h was calculated according to Eq. 2 and c~ was calculated with Method 1 (Amplitude equation) for reasons explained in Section 3.2.1. In Fig. 7 these calculated A values are compared with the A values as measured with the A probes for both within-row and between-row sites. The A probes at 0.03 m were used, the calculated A values represent the depth interval 0.03 to 0.05 m. The between-row PT-100's were used to calculate a. For all days, calculated A values were higher than measured values. Low measured values could be caused by poor contact between the probes and the soil, resulting from the loose character (dry conditions) of the soil and the presence of stones in the upper soil layer. The problem of contact resistance is discussed, among others, by Nagpal and Boersma (1973) and by van Haneghem (1981). According to van Haneghem (1981) the contact resistance, / ' , decreases with increasing temperature and decreasing particle diameter. In an experiment using silversand, moisture content had little effect on F. /" appears to be mainly determined by particle size and not by shape or stacking density. With an estimate of F, using data and formulae given in van Haneghem (1981) it was found that the error in A could lead to underestimation of around 0.10 W m - 1 K - i . The suggestion that the measured values are underestimated is supported by Ten Berge (1990) who shows that minimum values for mineral soils with 0 = 0 exhibit values varying from 0.15 to 0.30 W m -~ K -~ for sand to loamy sand. Since the sampled soil was not a pure sand and had 0 values slightly higher than 0.0, the values of around 0.10 (between-rows) appear too low. Values smaller than 0.10 can be reached, but only for substances containing a very high organic matter content (peat soils, forest litter).
12
A. Verhoef et al. / Agricultural and Forest Meteorology 78 (1996) 1-18 EFEDA
1991, vineyard
0.4
I
l
I
I
(a) 0.03
k~'E
rn
-0.12 m 0.3
I'~ I\
._>
I' I,
1''\
i i \ /.\.1 I. (.
0.2
- 0.22 m
I/
~,
J'
/
,,~,..
...... 0 . 3 5 m \
)\/--~/..~
.~
I ~-~
o o
E J~
I-
0.1
0 0.4
(b)
II
- 0.03 m I - - - 0.05 m ......... o.1o m
0.3
._>
I
....... 0.2
8
0.1
150
I
I
I
i.
I
155
160
165
170
175
180
Day number
Fig. 6. Measured (A probes) thermal conductivityfor the EFEDA-I measurement campaign. (a) Between row A. (b) Within-row A. 3.3.2. H A P E X - S a h e l , savanna 3.3.2.1. M e a s u r e d thermal conductivity. Fig. 8 shows the measured thermal conductivity
values at several depths during the HAPEX-Sahel campaign. Fig. 8(a) shows results for the vegetated profile and Fig. 8(b) the bare (nearly unvegetated) profile. In both graphs
A. Verhoef et al. / Agricultural and Forest Meteorology 78 (1996) 1-18
13
EFEDA 1992, vineyard i
0,6 Measured within-row ~, (-0.03) 0.5
Calculated ;L (Amplitude method, -0.04 m) \
"T
E
0,4
\
0.3 :
/ ~
\
~
)
o
/{:tv \~ x
0.2
1\
/_.
..
/
#_ 0.1
0 150
I
I
I
I
I
155
160
165
170
175
180
Day number Fig. 7. A comparisonbetween the measuredand calculated h values for the EFEDA-Imeasurementcampaign.
the variable course of A during the rainy period (day 230-265) is obvious, especially for the shallow sensors (0.015 and 0.04 m) where rapid wetting and drying alternate. After the rainstorms, A of all soil layers declines rapidly due to high evaporation rates during the drying out phase. The maximum values of A are around 2.0 W m -1 K - 1 (0 = +0.15 m 3 m-3). Minimum values are approximately 0.25 W m -~ K -1 ( 0 = _+0.02 m 3 m-3). The value of 0.25 is similar to the 'dry' A values of the sandy soils (Ten Berge, 1990). The ' w e t ' A value of 2.0 appears surprisingly high. The largest values of A for sands recorded are about 2.30 W m -~ K -1 under wet conditions (De Vries, 1963, 0 = 0.21 m 3 m-3; Riha et al., 1980, 0 = 0.38). The high A values observed for the HAPEX-Sahel experiment at relatively low moisture content might have been caused by the presence of termites, whose activity ensured a highly conducting soil. The agreement between the A values of the vegetated and the bare plot (about 5 m apart) is shown in Fig. 9 for a depth of 0.04 m with r 2 = 0.76. Differences between both plots are caused by soil heterogeneity (vegetation density, composition, moisture content), contact problems between the A probes and the soil, and different depths of both sensors caused by the rough surface. At low moisture content (low A values) the vegetated plot shows slightly higher A values, whereas for high A values the bare plot exhibits larger values of A. Both aspects can probably be explained by the presence of the vegetation, which preserves moisture during dry periods, but intercepts moisture during the wet periods. This same phenomenon has been observed for the EFEDA-I dataset.
14
A. Verhoef et al. / Agricultural and Forest Meteorology 78 (1996) 1-18
HAPEX-Sahel 1992, fallow savanna I
I
I
(a) 2.5 "T
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,,,,~ oo~
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270
280
290
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Fig. 8. Measured thermal conductivity during the HAPEX-sahel measurement campaign. (a) Vegetated soil plot. (b) Bare soil plot.
3.3.2.2. C a l c u l a t e d t h e r m a l c o n d u c t i u i t y . A comparison between the calculated and the
measured A is given in Fig. 10 for the bare and the vegetated plots. The A probes at 0.075 m depth were used. Calculated A values at that depth were obtained by linear interpolation of the a values between 0.05 and 0.10 m. This graph contains only a few
A. Verhoef et al. / Agricultural and Forest Meteorology 78 (1996) 1 - 18
15
HAPEX-Sahel 1992, savanna I
~,
I
•
I
I
2.5
E
J
2
x~
1:1-line
1.5
._~
o
E ~
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h-
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I
0
0.5
I
I
I
I
___
1 1.5 2 2.5 Thermal conductivity vegetated plot (WmIK "1)
Fig. 9. A comparison between the A values at 0.04 m. of the bare soil and vegetated plots.
HAPEX-Sahel 1992, savanna 3
I
2.5
I
•
I
i
vegetated plot J bare plot J
~
I
~
l
"
2
0.5
1:1-line 0
Z
0
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I
1 1.5 2 Calculated Z (WmIK 1)
I
2.5
3
Fig. 10. Comparison of calculated )t (ot.C h) against measured A (probe method) for the vegetated and bare soil plots. HAPEX-Sahel experiment, 0.075 m depth.
16
A. Verhoef et al. /Agricultural and Forest Meteorology 78 (1996) 1 - 1 8
HAPEX-Sahel
1992, s a v a n n a
I F
I
t
I
I
bare plot, calculated I - vegetated plot, measured -bare plot, measured
I
2.5
I
+ +
+
"T
E
2
"7 1.5 ~
~
_L.o j - °
~
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I
I
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0.06
0.08
0.1
0.12
0.14
Moisture content (m3m "3) Fig. ] 1. Measured and calculated thermal conductivity (HAPEX-Sahel experiment) as a function of soil
moisture content.
points due to missing data. Correlation between measured and calculated A values is satisfactory (r 2 = 0.85 and 0.78 for the vegetated and bare plots, respectively). Differences between measured and calculated thermal conductivities may be caused by two phenomena. At the first place, soil heterogeneity, causing differences in soil moisture content (especially influencing C h which has been measured nearly 50 m from the soil temperature/A profiles) and thus in thermal properties. Another possibility might be the problem of contact resistance, leading to too low measured values. It appeared, however, that differences between A-measured and A-calculated increased with increasing moisture content (see Fig. 11) which makes the latter cause less plausible. Horton (1982) argues that transient methods for determining the thermal conductivity (e.g. the A probes) are more applicable for measuring A of moist soils because a long waiting period for thermal gradients to become constant is not required (in contrast to steady-state methods). Thus water movement in response to temperature gradients is minimized, and the mechanism of heat transfer is almost exclusively by conduction. This might imply that measured A values in moist soils are closer to true conductivity values than they are in dry soils, thus explaining the phenomena observed in Fig. 10. Fig. 11 shows that the conductivities (measured and calculated) are a clear function of 0. The vegetated and bare plots show similar slopes. The slope of the calculated A - 0
A. Verhoef et al. / Agricultural and Forest Meteorology 78 (1996) 1-18
17
function is significantly higher whereas the intercept is smaller. A reason for this might be that C h a n d / o r ct estimates are too high during wet periods.
4. Conclusions Estimates of soil thermal properties have been obtained for 2 recent measurement campaigns in semi-arid regions: EFEDA-I and HAPEX-Sahel. It appeared that a combination of two PT-100 temperature sensors, installed at two depths close to the soil surface, and a soil moisture measurement provided sufficient information for calculation of C h (if an estimate of bulk density is available), A, and a. It was found that if soil temperature measurements are at hand, there is no need tO measure A directly with A probes. Its problems related to the contact resistance make it too uncertain whether reliable values of )t have been achieved. This was illustrated by the EFEDA-I data. The HAPEX-Sahel dataset showed a satisfactory agreement between /~measured and /~calculated' because of a finer soil texture and thus lower contact resistance. This underlines the fact that measuring )t separately is in most cases superfluous. Furthermore, it can be concluded that in fact all methods (except method 2 which calculated a constant a during both experiments) were reliable estimators of a , whereas Horton et al. (1983) showed that Methods 1, 2, 3 and 4 gave poor Or erratic values of a near the soil surface. Since there is good agreement between Method 6 and the other methods these (simpler) methods can be an useful tool in the estimation of a . However, for the HAPEX-Sahel experiment the Logarithmic method calculated too high values compared to the other method and for the EFEDA-I experiment the Arctangent equation yielded higher values. Therefore, it is concluded that the Amplitude and the Harmonic equation are the most reliable.
Acknowledgements The authors acknowledge F. Antonysen, C. van den Dries, A. Jansen, T. Jansen, W. Hillen, and D. Welgraven for their technical support. The students of the Department of Meteorology are thanked for their assistance with field measurements. This work was financially supported by the EC (EPOC-CT90-0030, EPOC-0024-C(CD)) and NWO (750.650.30 and 750.650.37). We also thank the Department of Water Resources (Wageningen Agricultural University) for placing their soil data (moisture content and bulk density) at our disposal. Dr. T. Lebel is acknowledged for his EPSAT rainfall data.
References Bolle, H.J., Andre, J.C., Arrue, J.L., Barth, H.K., Bessemoulin, P., Brasa, A., de Bruin, H.A.R., Cruces, J., Dugdale, G., Engman, E.T., Evans, D.L., Fantechi, R., Fiedler, F., van de Griend, A., Imeson, A.C., Jochum, A., Kabat, P., Kratzsch, T., Lagouarde, J.-P., Langer, I., Llamas, R., Lopez-Baeza, E., Melia Miralles, J., Muniosguren, L.S., Nerry, F., Noilhan, J., Oliver, H.R., Roth, R., Saatchi, S.S., Sanchez Diaz,
18
A. Verhoef et al. / Agricultural and Forest Meteorology 78 (1996) 1-18
J., de Santa Olalla, M., Shuttleworth, W.J., Sogaard, H., Stricker, H., Thornes, J., Vauclin, M. and Wickland, D., 1993. EFEDA: European field experiment in a desertification threatened area, Ann. Geophys., 11: 173-189. Droogers, P., v.d. Abeele, G.D., Cobbaert, J., Kim, C.P., Rbsslerov~i, R., Soet, M. and Stricker, J.N,M., 1993. Basic data sets description and preliminary results of EFEDA-Spain, Rapport 37. Vakgroep Waterhuishouding, Wageningen, The Netherlands, 103 pp. De Vries, D.A., 1963. Thermal properties of soils. In: W.R. van Wijk (Editor), Physics of Plant Environment. North-Holland, Amsterdam, pp. 210-233. Haneghem, I.A. van, 1981. Fen niet stationaire naaldmethode (warmtegeleiding, warmtecapaciteit, contactweerstand), Dissertation. Department of Physics, Wageningen Agricultural University, 187 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. Horton, R., 1982. Determination and use of soil thermal properties near the surface, Ph.D. Dissertation. New Mexico State University, Las Cruces, New Mexico, USA, 132 pp. Horton, R., Wierenga, P.J. and Nielsen, D.R., 1983. Evaluation of methods for determining the apparent thermal diffusivity of soil near the surface. Soil Sci. Soc. Am. J., 47: 25-32. Kimball, B.A. and Jackson, R.D., 1975. Soil heat flux determination: a null-alignment method. Agric. For. Meteorol., 15: 1-9. Nagpal, N.K. and Boersma, L., 1973. Air entrapment as a possible error in the use of a cylindrical heat probe. Soil Sci. Soc. Am. J., 37: 828-832. Riha, S.J., Mclnnes, K.J., Clids, S.W. and Campbell, G.S., 1980. A finite element calculation for determining thermal conductivity. Soil Sci. Soc. Am. J., 44: 1323-1325. Seemann, J., 1979. Measuring technology. In: J. Seemann et al. (Editors), Agrometeorology. Springer-Verlag, Berlin, pp. 40-45. Sene, K.J., 1994. Parameterisations for energy transfers from a sparse vine crop. Agric. For. Meteorol., 71: 1-18. Soet, M., Droogers, P., Jaarsma, M.N., Kim, C.P., Monincx, J.F. and Stricker, J.N.M., 1993. HAPEX-SaheI: Basic description of methods and datasets, Rapport 43. Vakgroep Waterhuishouding, Wageningen, The Netherlands, 50 pp. Tanner, C.B., 1963. Basic instrumentation and measurements for plant environment and micrometeorolgy, Soil Bull. 6. University of Wisconsin, Madison, WI. Ten Berge, H.F.M., 1990. Heat and water transfer in bare topsoil and the lower atmosphere, Sire. Monogr. 33. Pudoc, Wageningen, The Netherlands, 207 pp. Van Loon, W.K.P., 1991. Heat and mass transfer in frozen porous media, Ph.D. Thesis. Wageningen Agricultural University, Wageningen, The Netherlands, 204 pp. Wijk, W.R., van, 1963. Physics of plant environment. North-Holland, Amsterdam, 382 pp.
AGRICULTURAL AND FOREST METEOROLOGY Agricultural and Forest Meteorology 78 (1996) 1-18
Thermal soil properties for vineyard (EFEDA-I) and savanna (HAPEX-Sahel)sites Anne Verhoef *, Bart J.J.M. van den Hurk, Adrie F.G. Jacobs; Bert G. Heusinkveld • Department of Meteorology, Wageningen Agricultural University, Duivendaal 2, 6701 AP Wageningen, The Netherlands
Received 30 March 1995; accepted 21 April 1995
Abstract
This paper describes the course of topsoil thermal conductivity, A, diffusivity, at, and heat capacity, C h, during two measurement campaigns, conducted in semi-arid areas--the EFEDA-I experiment and HAPEX-Sahel. For the derivation of a , five methods (the Amplitude, Phase, Arctangent, Logarithmic and Harmonic equation) were compared. Values of C h were derived from measurements of soil moisture content, 8, and dry bulk density. A was either measured directly (the non-stationary probe method) or calculated from A = a . C h. Thermal soil properties were clearly related to 0 (and thus rainfall) throughout the measurement campaigns: hardly any changes occurred during the EFEDA-I experiment where continuous dry conditions prevailed, whereas for HAPEX-Sahel a clear decrease in all thermal properties was observed after the last rainfall. For calculation of ct, the Amplitude and the Harmonic equation gave the best results. Calculation of at and A beneath the vegetation plots yielded unreliable results, mainly due to shading effects causing more than one temperature maximum. : Direct measurement of A yielded unrealistically low values for the dry soil conditions as encountered in Spain, due to poor contact between.probe and s o i l A correction for the contact resistance is necessary to obtain better estimates. For HAPEX-Sahel, measured and calculated A values were much closer, mainly for reasons of higher 0 values and a high soil compaction which ensured better contact between soil and probes.
* Corresponding author at: Institute of Hydrology, Crowmarsh Gifford, Wallingford, Oxon OX10 8BB, UK. 0168-1923/96/$15.00 © 1996 Elsevier Science B.V. All fights reserved SSDI 0 1 6 8 - 1 9 2 3 ( 9 5 ) 0 2 2 5 4 - 6
2
A. Verhoefet al./Agricultural and Forest Meteorology 78 (1996) 1-18
I. Introduction
If advection and storage are neglected, the soil heat flux density, G, is one of the four components of the surface energy balance:
R.=~+LE+~
(1)
where R , is the net radiation, H is the sensible heat flux, and LE is the latent heat flux caused by vaporization (all fluxes are in W m - Z ) . In the case of a closed, well-watered canopy the soil heat flux is usually relatively small and parameterized as a fraction of R n (0.1-0.2, depending on the type of crop and soil moisture content). For sparse canopies under semi-arid or arid conditions, however, G can account for a large part of the energy balance (up to 40% of R n) and being equal to or even higher than LE. Under these circumstances accurate estimates of G should be obtained. G is determined by the thermal soil properties (thermal conductivity, A, heat capacity, C h, and apparent thermal diffusivity, a ) which are in turn dependent on soil moisture content, 0, soil composition and vegetation cover (shading, root influence on 0). These thermal soil properties vary in space causing heterogeneity and in time. Although heterogeneity plays a role for closed canopies in temperate climates, its influence on G is much larger for sparse canopies. Two types of heterogeneity can be distinguished which are important for micrometeorological investigations. First, meso-scale heterogeneity can be induced by spatially variable rainfall which influences A, C h and a (and thus G) through changes in moisture content on a scale of several kilometres. The second type is heterogeneity on the micro-scale, which is especially important for sparse canopies. This arises because the total soil surface is composed of soil under the open (bare, or slightly vegetated) patches in between the isolated plants/bushes and soil located under the canopy. The vegetation will influence the underlying soil in two ways; it will shade it and it will influence 0, and thus thermal soil properties and soil heat flux. Besides spatial variation, a large temporal variation is expected if heavy rainfall is alternated by severe droughts. The recently conducted EFEDA-I and HAPEX-Sahel experiments provided an excellent opportunity to study the spatial (meso-scale and micro-scale) and temporal variability of the thermal properties and G for sparsely vegetated areas. This paper describes the thermal properties of two soils (located in a vineyard and a savanna, respectively) which were sampled during the above-mentioned experiments. An appraisal is made of the changes during the growing season (temporal variability), resulting from soil drying. The impact of changing moisture conditions and effects of shading on thermal soil properties on the spatial micro-scale (below and in between canopy elements) is also investigated. The values of A, o~ and C h, derived here, can be used as input in SVATs or GCMs.
A. Verhoef et al. /Agricultural and Forest Meteorology 78 (1996) 1-18
3
2. Materials and methods
2.1. Site description and soil characteristics 2.1.1. EFEDA-I, vineyard The EFEDA-I experiment was conducted in Tomelloso (Spain, latitude 2°55'48" N, longitude 39008'30 " E) during June 1991 (Bolle et al,, 1993). The soil measurements were collected at the Wageningen Agricultural University Meteorological site, which was located in a sparsely vegetated vineyard (Vitis Vinifera L. cv. variety: Airen), with row-spacings of 2.5 m and between-plant spacings of about 2.0 m. The topsoil consisted of a reddish sandy loam, sparsely covered with stones with a maximum diameter of 3 cm. The layer from 25-35 cm was a silt loam, whereas the other layers were sandy loams (Droogers et al., 1993). In June, the upper soil layers were already dry. The last rainfall (0.5 mm) occurred on June 4 (day 155). In the preceding week about 30 mm of precipitation was recorded (Sene, 1994). Soil temperatures were sampled with PT-100 resistance probes, which were developed at the Department of Meteorology, Wageningen. Soil temperatures below the between-row bare soil surface were measured at 5 depths: 0.03, 0.05, 0.10, 0.25 and 0.50 m. To measure the soil temperatures below the canopy, 5 resistance thermometers were inserted at the same depths north of a vineplant at a distance of 0.3 m from the trunk. The soil moisture content, 0, was measured by TDR sensors at depths of 0.10, 0.20, 0.30, 0.40 and 0.50 m, where the dry bulk density, Pd, was found to be 1340, 1200, 1240, 1210 and 1190 k g m -3 (Droogers et al., 1993). At 0.10 m depth 0 varied from 0.08 to 0.06 m 3 m -3 during the measurement campaign. For deeper layers values of up to 0.18 were recorded with little variation during the season (Fig. l(a)). So-called non-steady-state probes (Van Loon, 1991), developed at the Department of Meteorology, Wageningen, were used to measure thermal conductivity. Two thermal conductivity profiles were sampled twice a day. One was located in the vicinity of a plant with probes at depths of 0.03, 0.05, 0.10, and 0.20 m. The probes located between two rows were installed at depths of 0.03, 0.12, 0.22, and 0.35 m.
0.25
FOAgvnyr=: (a)
o~
........
~E ~, o.1s
~
o 150
Fig.
]. Soil
Hapcx-Sahc]
os HAPEXSh 9 vinn II
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~-:":'::-'-'~-"~'-~:-'~::-~=':.:::'.~
i
r
i
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160
165 Day number
170
175
moisture campaign
content, (b).
0, at several
(b)
~ ~l=
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~
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o 180
depths during t h e
--O.06m ~ -o.lOm
.... ~ .... . . . . . 0.40-0.50 rn ~
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/...,
.
i
i
i
i
240
250
260 Oar/ number
270
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280
290
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A. Verhoefet al./Agricultural and Forest Meteorology 78 (1996) 1-18
4
HAPEX-Sahel 1992, 70
savanna
JllllEIIIILIIIIILIIlillllllPkLIllli[llllllllllllliklllllliillllllBIIllLIIL
60 50 E E
40
~
30 20
10
Day number
Fig. 2. Precipitation during the HAPEX-Sahelmeasurementcampaign. For the assessment of a , continuous measurements of soil temperatures were needed which were only available for the days of June 5, 6, 9, 12, 17, 20, 24, 25, 26 and 29. For the other days values were interpolated. 2.1.2. HAPEX-Sahel, savanna
The HAPEX-Sahel experiment (Goutorbe et al., 1994) took place in Niger from August until October 1992. Results are presented for the so-called Central West Site, 50 km east of Niamey (latitude 13°32'60" N, longitude 2o30'68" E). The savanna consisted of scattered shrubs (Guiera senegalensis) with an undergrowth of several species of grasses and herbs. Because of the late start of the rainy season (end of June) the understorey remained rather sparse and low (maximum height 0.5 m). The soil was classified as a loamy sand (Soet et al., 1993). The ~d was measured as 1600, 1580, 1480 and 1400 k g m -3 for the depths of 0.05, 0.10, 0.25 and 0.45 m, respectively (Soet et al., 1993). The larger Pa values, compared to the EFEDA-I experiment, are a result of higher sand contents and a higher soil compaction possibly caused by the excrements of termites. As a result of frequent rainfall (Fig. 2) temporal variability of soil moisture was large, compared to EFEDA, with 0 varying from 0.16 m 3 m -3 after a rainstorm to 0.03 m 3 m -3 during a drying period (Fig. l(b)). Soil temperatures were measured with horizontally inserted PT-100 resistance thermometers at two plots in close proximity. One of the plots was hardly vegetated ('bare' plot) whereas the other plot exhibited
A. Verhoef et aL / Agricultural and Forest Meteorology 78 (1996) 1-18
5
more vegetation (grass and herbs) than average. Each temperature array consisted of 5 thermometers installed at depths of 0.03, 0.05, 0.10, 0.25, and 0.50 m. The A probes were placed in between the temperature sensors, at depths of 0.015, 0.04, 0.075, and 0.15 m. For reading, they were connected to a portable datalogger several times per day (3 times during the wet period, 1 or 2 times during the drying period).
2.2. Theory of thermal soil properties Surface soil heat fluxes can be estimated with several methods of which the most commonly used are the Calorimetric, Gradient, Harmonic and Plate method (Tanner, 1963; Kimball and Jackson, 1975; Ten Berge, 1990), All methods require the installation of at least 1 thermometer (Plate method, Harmonic method) or more (2 for the Gradient method and several, at least 4 or 5, for the Calorimetric method). The Plate method uses thermopile flux plates. Furthermore, it demands an estimate of heat storage of the soil layer above the sensor. Besides measurements of temperature or the flux at a certain depth, an estimate of the soil thermal properties (A, a and C h) is needed. The Calorimetric method requires estimates of C h, whereas for the Gradient and the Plate method values of A and C h (calculation of storage) are required. For the Harmonic method all thermal properties are used. Besides careful installation and depth location of the sensors and minimum disturbance of the soil, much attention has therefore to be paid to the determination of the thermal soil properties.
2.2.1. Volumetric heat capacity The volumetric heat capacity, C h, is defined as the change of heat content per soil volume and per change of temperature (J m - 3 K - ~). It can be calculated if values for bulk density and moisture content for the soil layer under consideration, using C h = ECh,i~)i
(2)
i
where Ch, i is the volumetric heat capacity for each soil component and q~; is the volume fraction of component i. Organic matter and air were not taken into account because their contribution is neglible. The volumetric heat capacities for the mineral soil components, C,,s, and water, Ch., are 2.0, and 4.2 MJm -3 K - i , respectively (Ten Berge, 1990). With knowledge of the water and solid phase fractions, C h for the upper soil layer can be calculated using b
Ch = C h , s Pd - - + Ch,lO Ps
(3)
where Ps is the density of the solid phase (kgm -3) and ~9d the dry bulk density (kg m - 3). Ps was taken as 2650 kg m - 3.
6
A. Verhoefet al./Agricultural and Forest Meteorology 78 (1996) 1-18
2.2.2. Thermal diffusivity The soil thermal diffusivity, a (m 2 s-1), is the ratio of thermal conductivity to the volumetric heat capacity: c~ = A / C h
(4)
Horton et al. (1983) evaluated 6 methods for determining ct. For the calculation of ct for the two data-sets five of their methods will be applied, viz. the Amplitude equation, the Phase equation, the Arctangent equation, the Logarithmic equation and the Harmonic equation. The equation describing the conductive heat transfer in a one-dimensional isotropic medium is given by
6T - -
6t
82T -
(5)
6z 2
In this case a is independent of depth and time. Using the Fourier series representation, soil temperature near the soil surface can be described by a sum of sine and cosine terms according to the following equation M
T ( t ) = T + E [ A,cos(no~t) + Bnsin(noJt)]
(6)
n=l
where the overbar denotes an average in the time interval considered, M is the number of harmonics and A n and B n are the amplitudes, o~ is the radial frequency ( = 27r/P), with P representing the period of the fundamental cycle. The following formulas base their calculation of a on simplifications (analytical solutions) of Eq. 5 applying Eq. 6 (with different values for M) to describe the temperature.
2.2.2,1. Method 1. The Amplitude equation. The amplitude equation is given by
=2
[z2z]2 In AT?-A2
(7)
where A 1 and A 2 a r e the amplitudes at depths z~ and z2, respectively. Determination of a from this equation requires measurement of the maximum and minimum temperature at both depths during the period of the fundamental cycle (in our case 24 h).
2.2.2.2. Method 2. The Phase equation. The Phase equation is given by a=
1 [z2-zj] 2 2---~[ 6t l
(8)
in which 6 t ( = t 2 - t 1) signifies the time interval between the measured occurrences of maximum soil temperature at depths zl and z2-
A. Verhoef et al. / Agricultural and Forest Meteorology 78 (1996) 1-18
7
2.2.2.3. Method 3. The Arctangent equation. With M = 2, the apparent thermal diffusivity can be calculated from
o,( z2 - z,)2 2 arctan (T,
r3)(r;
(9) T,)(T;
T/~)
where temperatures T~ and T" are recorded every 6 h (subscripts 1 to 4) at two depths, z~ and z2 (denoted by '), respectively.
2.2.2.4. Method 4. The Logarithmic equation. It was shown by Seemann (1979) that, in analogy to Method 3, the apparent thermal diffusivity can also be calculated from a=
[
0.0121(z2 - z,)
(10)
In (T1- T3)2 "~-(T2S T4)2
2.2.2.5. Method 5. The Harmonic equation. The analytical solution of Eq. 5 according to van Wijk (1963) is
M T(z,t)=T+
~ (Co,e-Z~-L-7~sin(ntot+qbo,-Z~))
n=l
(11)
where Con and ~b0n are the amplitude and phase angle of the n th harmonic for the upper boundary, respectively (Horton et al., 1983). The harmonic analysis of temperatures at zi will yield M values of Con and ~bon which can give an estimate of temperature at z2 (provided the soil is homogeneous in the vertical) with the help of Eq. 11, if a proper value of a is given. ot can be found by selecting an a (through iteration) which gives the smallest sum of squared differences between the measured and estimated temperature at z2. The sum of squares will be composed of 24 whole (0,1,2 . . . . . 24) or half-hour (0.5,1.5 . . . . . 23.5) differences between measured and calculated temperature.
2.2.3. Thermal conductivity Thermal conductivity, A (W m - ~ K - ~), was measured directly using non-steady-state probes (Van Loon, 1991). Furthermore, it was calculated by Eq. 4.
3. Results 3.1. Soil heat capacity 3.1.1. EFEDA-I, vineyard Fig. 3(a) gives the variation of C h at 5 depths. After the last rainfall, maximum values of around 1.6 M J m -3 K - 1 w e r e reached at depths of 0.30 and 0.50 m. The
8
A. Verhoefet al./Agricultural and ForestMeteorology 78 (1996) 1-18 EFEDA 1991,
vineyard
HAPEX-Sahel 2
(a)
i I (b)
,
1992, ,
savanna ,
, I- -
, OXO-O,OS m
I
1.8
1.8 ~
?"
1.6
~
-
~6
t ~,
p.......... .....
~.
.~.
r~
~ ;":':~'~' ..
o.10-o,25 m
........ o
"~" "Z'" " ~,.- ..:. ~::.:.,......
25-o,5o m
12
1 S0
155
160
165
170
Day n u m b e r
175
180
230
240
250
~60
2 ]0
280
290
Day number
Fig. 3. Heat capacity as calculated with Eq. 2 for the EFEDA-I measurement campaign (a) and for the HAPEX-Sahel experiment (b). minimum value was about 1.1 M J m -3 K -1. After day 160, C h remains more or less constant for all soil layers, which is caused by the small changes in 0. Soil layering may cause C h to change abruptly with depth. 3.1.2. HAPEX-Sahel, savanna
The variation of heat capacity during the campaign is shown in Fig. 3(b) for 4 depths. During the rainy period maximum values of 1.7 M J m -3 K -1 were attained. The minimum value was about 1.2 MJ m -3 K - t for the upper depth, occurring 3 weeks after the last rainstorm. Both experiments show a comparable range of C h values. Nevertheless, the values in the upper soil layers for the HAPEX-Sahel experiment during the first half of the campaign were considerably higher than those during the EFEDA-I experiment as a result of wet soil conditions. This led to a large temporal variability for the HAPEX-Sahel experiment. 3.2. Soil diffusivity
Thermal diffusivity was only calculated for the top 10 cm of soil (from the harmonic analysis of temperature at 0.03 m depth, the a values at 0.05 and 0.10 m were derived). The reason for this is that attempts to calculate a for 0.25 and 0.50 m (with the Harmonic equation which, according to Horton et al. (1983), is the most reliable method to calculate or) yielded unrealistic values, which implies that the soil was probably not homogeneous in the vertical direction. However, for calculation of G we only need a value for a at the upper few centimetres of soil, and we can possibly assume the first 10 cm of the soil to be uniform. 3.2.1. EFEDA-I, vineyard
The thermal diffusivity of the between-row soil at 0.05 m depth is given in Fig. 4(a) (temperatures at half-hour intervals of time were used). The Phase equation is not shown: it appeared that this method calculated a constant ct during the entire period
A. Verhoef et al. / Agricultural and Forest Meteorology 78 (1996) 1-18 EFEDA
1991,
HAPEX-Sahel
vineyard 2
1992,
9
savanna
(hi i
%
"
i
H a t r n o m ¢ n~lhod
- --
- ~'et=ng~mt
-
-- - Lt~arlthtr~
l .-...- I
m~hod method
~_ os
~_ o.s
0 1 SO
[
i
i
155
160
~6 5
Day
number
_
i
i
170
175
0 180
l
230
240
-
-
[
~
L
-
-
250
.
260
Day
l
270
_
[
280
-
-
[
number
Fig. 4. Course of thermal diffusivity, according to several methods, during the EFEDA-I measurement campaign (a) and during the HAPEX-Sahel measurement campaign (b).
because the 1-hour resolution of temperatures resulted in the same value of ~ t (see Eq. 8) for all days. All methods show a similar course: after the last occurrence of rain (day 154), a decreases rapidly to a more-or-less constant value. Some dewfall on day 168 and 169 appears to influence soil moisture content (and thus a ) to some extent. The sudden increase after day 177 is caused by artificial wetting of the soil temperature plot, which was done to obtain a larger range of 0 values for derivation of the thermal soil properties. The Amplitude, Logarithmic and Harmonic equation calculate low, but mutually consistent, a values during the dry period ( ~ 0.25 mm 2 s - 1). The Arctangent method is approximately 2 times higher. The Harmonic method exhibits relatively high a values (between day 171-176), which cannot be related with increased moisture content. For these days (not shown) the summed difference between the measured and fitted temperature at 0.05 m is large (the fitted temperature consistently overestimating the daytime measured temperature). This large difference between observed and fitted temperature was always accompanied with high soil temperatures. This same, relatively large, discrepancy between fitted and observed temperatures for hot, relatively dry soils has been observed for the HAPEX-Sahel experiment. Four explanations for this can be suggested. • After rainfall, part of the soil heat flux is being used for soil evaporation. This would make the temperatures at 0.05 m cooler than expected from Fourier analysis of the temperatures at 0.03 m (if the evaporation front lies between 0.03 and 0.05 m). If the PT-100 at 0.05 m is in fact placed at a deeper depth this fact is obscured by the evaporation. A change in soil composition or density occurs below 0.03 m. • The occurrence of a change of a during the day; because of diurnal fluctuation in 0, a is expected to be higher during the morning and lower during the afternoon. The assumed validity of sinusoidal variation. Shading of the soil by the vines (thus causing two temperature maxima) led to anomalous within-row values of a. These values are therefore not presented here.
1o
A. Verhoef et al. / Agricultural and Forest Meteorology 78 (1996) 1-18
HAPEX-Sahel
~
1992, s a v a n n a
I
1
I
I
I
I
I
I
I
I
I
I
0.02
0.04
0.06
0.08
0.1
0.12
1.5
E >
0.5
0
0
0.14
Soil moisture content (m3m"3)
Fig. 5. Relationship between soil moisture content and calculated (Harmonic method) diffusivity for the HAPEX-Sahel experiment. 3.2.2. HAPEX-Sahel, savanna
Fig. 4(b) gives the a values during the campaign obtained from Method 1, 3, and 4 using hourly mean values for soil temperature. During the rainy period, a reaches maximum values of around 1.5 mm 2 s -~ . This value is high but not unusual for wet sandy soils. It agrees with the high A values found for this soil at relatively low 0 values (See Section 3.3.2). A few days without rainfall (e.g. between day 244 and 250) led to a considerable decrease of ct. This is caused by the high evaporative demand of this region, which lowered 0 rapidly. After the beginning of the dry season, a rapidly declines to values around 0.3 mm 2 s -1. To investigate the dependence of a on the choice of the temperature value used, the diffusivity was also calculated with 24 half hourly mean values as input (not shown). It appeared that the Amplitude method is most influenced by this change, having a more irregular character, indicating that the maximum a n d / o r minimum temperatures are probably lying closer to the whole hours than to the half-hours. The Logarithmic equation, although giving a temporal variation similar to the other methods, was much higher and is therefore not shown in these graphs. If a is plotted against moisture content at 0.05 m a clear linear relationship is found (Fig. 5, r E = 0.80). This supports the validity of our calculations. For the EFEDA-I dataset there was insufficient variation in 0 to show a relationship between 0 and ct. Temperature profiles were also measured underneath a more vegetated soil plot. Attempts to calculate a for this location led to erratic and illogical results for all methods. This was caused by the irregular temperature profiles (caused by
A. Verhoef et al./Agricultural and Forest Meteorology 78 (1996) 1-18
11
the vegetation) and by the fact that the actual depth at which the sensors were located deviated considerably from the intended installation depth. This discrepancy might have been the result of soil movement caused by severe flooding during several rainstorms. 3.3. Soil thermal conductivity 3.3.1. E F E D A - L vineyard 3.3.1.1. Measured thermal conductivity. The directly measured values of A at 4 depths
are given in Fig. 6(a) (between-row) and (b) (within-row) for the entire measurement campaign. It appears that within-row h values are slightly higher than the values for the between-row soil, possibly shading reduces soil evaporation. Furthermore, the curves reflect that after day 155 the soil moisture content soon reached an equilibrium value (cf. Fig. l(a)). The large differences in observed A between days 154 and 155 may be the result of the last rainstorm on day 153. On these days, the between-row h value is higher than the within-row h value, probably as a result of the sheltering effect of the vineplants. Vertical and horizontal redistribution of soil moisture and reduced evaporation rates from the soil in the vicinity of the plants result in the between-row A value being lower than the within-row h value for the rest of the campaign. The values for the within-row A sensor at a depth of 0.20 m were clearly deviating (even taking into account the higher 0 values) from those for the other probes and are therefore not shown in Fig. 6(b). 3.3.1.2. Calculated thermal conductivity. Values of A were also derived from Eq. 4,
where C h was calculated according to Eq. 2 and c~ was calculated with Method 1 (Amplitude equation) for reasons explained in Section 3.2.1. In Fig. 7 these calculated A values are compared with the A values as measured with the A probes for both within-row and between-row sites. The A probes at 0.03 m were used, the calculated A values represent the depth interval 0.03 to 0.05 m. The between-row PT-100's were used to calculate a. For all days, calculated A values were higher than measured values. Low measured values could be caused by poor contact between the probes and the soil, resulting from the loose character (dry conditions) of the soil and the presence of stones in the upper soil layer. The problem of contact resistance is discussed, among others, by Nagpal and Boersma (1973) and by van Haneghem (1981). According to van Haneghem (1981) the contact resistance, / ' , decreases with increasing temperature and decreasing particle diameter. In an experiment using silversand, moisture content had little effect on F. /" appears to be mainly determined by particle size and not by shape or stacking density. With an estimate of F, using data and formulae given in van Haneghem (1981) it was found that the error in A could lead to underestimation of around 0.10 W m - 1 K - i . The suggestion that the measured values are underestimated is supported by Ten Berge (1990) who shows that minimum values for mineral soils with 0 = 0 exhibit values varying from 0.15 to 0.30 W m -~ K -~ for sand to loamy sand. Since the sampled soil was not a pure sand and had 0 values slightly higher than 0.0, the values of around 0.10 (between-rows) appear too low. Values smaller than 0.10 can be reached, but only for substances containing a very high organic matter content (peat soils, forest litter).
12
A. Verhoef et al. / Agricultural and Forest Meteorology 78 (1996) 1-18 EFEDA
1991, vineyard
0.4
I
l
I
I
(a) 0.03
k~'E
rn
-0.12 m 0.3
I'~ I\
._>
I' I,
1''\
i i \ /.\.1 I. (.
0.2
- 0.22 m
I/
~,
J'
/
,,~,..
...... 0 . 3 5 m \
)\/--~/..~
.~
I ~-~
o o
E J~
I-
0.1
0 0.4
(b)
II
- 0.03 m I - - - 0.05 m ......... o.1o m
0.3
._>
I
....... 0.2
8
0.1
150
I
I
I
i.
I
155
160
165
170
175
180
Day number
Fig. 6. Measured (A probes) thermal conductivityfor the EFEDA-I measurement campaign. (a) Between row A. (b) Within-row A. 3.3.2. H A P E X - S a h e l , savanna 3.3.2.1. M e a s u r e d thermal conductivity. Fig. 8 shows the measured thermal conductivity
values at several depths during the HAPEX-Sahel campaign. Fig. 8(a) shows results for the vegetated profile and Fig. 8(b) the bare (nearly unvegetated) profile. In both graphs
A. Verhoef et al. / Agricultural and Forest Meteorology 78 (1996) 1-18
13
EFEDA 1992, vineyard i
0,6 Measured within-row ~, (-0.03) 0.5
Calculated ;L (Amplitude method, -0.04 m) \
"T
E
0,4
\
0.3 :
/ ~
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~
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o
/{:tv \~ x
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1\
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/
#_ 0.1
0 150
I
I
I
I
I
155
160
165
170
175
180
Day number Fig. 7. A comparisonbetween the measuredand calculated h values for the EFEDA-Imeasurementcampaign.
the variable course of A during the rainy period (day 230-265) is obvious, especially for the shallow sensors (0.015 and 0.04 m) where rapid wetting and drying alternate. After the rainstorms, A of all soil layers declines rapidly due to high evaporation rates during the drying out phase. The maximum values of A are around 2.0 W m -1 K - 1 (0 = +0.15 m 3 m-3). Minimum values are approximately 0.25 W m -~ K -1 ( 0 = _+0.02 m 3 m-3). The value of 0.25 is similar to the 'dry' A values of the sandy soils (Ten Berge, 1990). The ' w e t ' A value of 2.0 appears surprisingly high. The largest values of A for sands recorded are about 2.30 W m -~ K -1 under wet conditions (De Vries, 1963, 0 = 0.21 m 3 m-3; Riha et al., 1980, 0 = 0.38). The high A values observed for the HAPEX-Sahel experiment at relatively low moisture content might have been caused by the presence of termites, whose activity ensured a highly conducting soil. The agreement between the A values of the vegetated and the bare plot (about 5 m apart) is shown in Fig. 9 for a depth of 0.04 m with r 2 = 0.76. Differences between both plots are caused by soil heterogeneity (vegetation density, composition, moisture content), contact problems between the A probes and the soil, and different depths of both sensors caused by the rough surface. At low moisture content (low A values) the vegetated plot shows slightly higher A values, whereas for high A values the bare plot exhibits larger values of A. Both aspects can probably be explained by the presence of the vegetation, which preserves moisture during dry periods, but intercepts moisture during the wet periods. This same phenomenon has been observed for the EFEDA-I dataset.
14
A. Verhoef et al. / Agricultural and Forest Meteorology 78 (1996) 1-18
HAPEX-Sahel 1992, fallow savanna I
I
I
(a) 2.5 "T
E
2 •
1.5
• XO QX~x
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0.040 m 0.075 m 0.15m
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i~
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•
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x
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OOooO
¢
.~,,.
• I
1
240
250
•
,,,,~ oo~
•
o
• I
.....
260
I
270
280
290
Day number
Fig. 8. Measured thermal conductivity during the HAPEX-sahel measurement campaign. (a) Vegetated soil plot. (b) Bare soil plot.
3.3.2.2. C a l c u l a t e d t h e r m a l c o n d u c t i u i t y . A comparison between the calculated and the
measured A is given in Fig. 10 for the bare and the vegetated plots. The A probes at 0.075 m depth were used. Calculated A values at that depth were obtained by linear interpolation of the a values between 0.05 and 0.10 m. This graph contains only a few
A. Verhoef et al. / Agricultural and Forest Meteorology 78 (1996) 1 - 18
15
HAPEX-Sahel 1992, savanna I
~,
I
•
I
I
2.5
E
J
2
x~
1:1-line
1.5
._~
o
E ~
0.5
h-
0
I
0
0.5
I
I
I
I
___
1 1.5 2 2.5 Thermal conductivity vegetated plot (WmIK "1)
Fig. 9. A comparison between the A values at 0.04 m. of the bare soil and vegetated plots.
HAPEX-Sahel 1992, savanna 3
I
2.5
I
•
I
i
vegetated plot J bare plot J
~
I
~
l
"
2
0.5
1:1-line 0
Z
0
0.5
I
I
I
1 1.5 2 Calculated Z (WmIK 1)
I
2.5
3
Fig. 10. Comparison of calculated )t (ot.C h) against measured A (probe method) for the vegetated and bare soil plots. HAPEX-Sahel experiment, 0.075 m depth.
16
A. Verhoef et al. /Agricultural and Forest Meteorology 78 (1996) 1 - 1 8
HAPEX-Sahel
1992, s a v a n n a
I F
I
t
I
I
bare plot, calculated I - vegetated plot, measured -bare plot, measured
I
2.5
I
+ +
+
"T
E
2
"7 1.5 ~
~
_L.o j - °
~
o
E
1
0.5
0
I
0
0.02
I
I
1
I
I
0.04
0.06
0.08
0.1
0.12
0.14
Moisture content (m3m "3) Fig. ] 1. Measured and calculated thermal conductivity (HAPEX-Sahel experiment) as a function of soil
moisture content.
points due to missing data. Correlation between measured and calculated A values is satisfactory (r 2 = 0.85 and 0.78 for the vegetated and bare plots, respectively). Differences between measured and calculated thermal conductivities may be caused by two phenomena. At the first place, soil heterogeneity, causing differences in soil moisture content (especially influencing C h which has been measured nearly 50 m from the soil temperature/A profiles) and thus in thermal properties. Another possibility might be the problem of contact resistance, leading to too low measured values. It appeared, however, that differences between A-measured and A-calculated increased with increasing moisture content (see Fig. 11) which makes the latter cause less plausible. Horton (1982) argues that transient methods for determining the thermal conductivity (e.g. the A probes) are more applicable for measuring A of moist soils because a long waiting period for thermal gradients to become constant is not required (in contrast to steady-state methods). Thus water movement in response to temperature gradients is minimized, and the mechanism of heat transfer is almost exclusively by conduction. This might imply that measured A values in moist soils are closer to true conductivity values than they are in dry soils, thus explaining the phenomena observed in Fig. 10. Fig. 11 shows that the conductivities (measured and calculated) are a clear function of 0. The vegetated and bare plots show similar slopes. The slope of the calculated A - 0
A. Verhoef et al. / Agricultural and Forest Meteorology 78 (1996) 1-18
17
function is significantly higher whereas the intercept is smaller. A reason for this might be that C h a n d / o r ct estimates are too high during wet periods.
4. Conclusions Estimates of soil thermal properties have been obtained for 2 recent measurement campaigns in semi-arid regions: EFEDA-I and HAPEX-Sahel. It appeared that a combination of two PT-100 temperature sensors, installed at two depths close to the soil surface, and a soil moisture measurement provided sufficient information for calculation of C h (if an estimate of bulk density is available), A, and a. It was found that if soil temperature measurements are at hand, there is no need tO measure A directly with A probes. Its problems related to the contact resistance make it too uncertain whether reliable values of )t have been achieved. This was illustrated by the EFEDA-I data. The HAPEX-Sahel dataset showed a satisfactory agreement between /~measured and /~calculated' because of a finer soil texture and thus lower contact resistance. This underlines the fact that measuring )t separately is in most cases superfluous. Furthermore, it can be concluded that in fact all methods (except method 2 which calculated a constant a during both experiments) were reliable estimators of a , whereas Horton et al. (1983) showed that Methods 1, 2, 3 and 4 gave poor Or erratic values of a near the soil surface. Since there is good agreement between Method 6 and the other methods these (simpler) methods can be an useful tool in the estimation of a . However, for the HAPEX-Sahel experiment the Logarithmic method calculated too high values compared to the other method and for the EFEDA-I experiment the Arctangent equation yielded higher values. Therefore, it is concluded that the Amplitude and the Harmonic equation are the most reliable.
Acknowledgements The authors acknowledge F. Antonysen, C. van den Dries, A. Jansen, T. Jansen, W. Hillen, and D. Welgraven for their technical support. The students of the Department of Meteorology are thanked for their assistance with field measurements. This work was financially supported by the EC (EPOC-CT90-0030, EPOC-0024-C(CD)) and NWO (750.650.30 and 750.650.37). We also thank the Department of Water Resources (Wageningen Agricultural University) for placing their soil data (moisture content and bulk density) at our disposal. Dr. T. Lebel is acknowledged for his EPSAT rainfall data.
References Bolle, H.J., Andre, J.C., Arrue, J.L., Barth, H.K., Bessemoulin, P., Brasa, A., de Bruin, H.A.R., Cruces, J., Dugdale, G., Engman, E.T., Evans, D.L., Fantechi, R., Fiedler, F., van de Griend, A., Imeson, A.C., Jochum, A., Kabat, P., Kratzsch, T., Lagouarde, J.-P., Langer, I., Llamas, R., Lopez-Baeza, E., Melia Miralles, J., Muniosguren, L.S., Nerry, F., Noilhan, J., Oliver, H.R., Roth, R., Saatchi, S.S., Sanchez Diaz,
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A. Verhoef et al. / Agricultural and Forest Meteorology 78 (1996) 1-18
J., de Santa Olalla, M., Shuttleworth, W.J., Sogaard, H., Stricker, H., Thornes, J., Vauclin, M. and Wickland, D., 1993. EFEDA: European field experiment in a desertification threatened area, Ann. Geophys., 11: 173-189. Droogers, P., v.d. Abeele, G.D., Cobbaert, J., Kim, C.P., Rbsslerov~i, R., Soet, M. and Stricker, J.N,M., 1993. Basic data sets description and preliminary results of EFEDA-Spain, Rapport 37. Vakgroep Waterhuishouding, Wageningen, The Netherlands, 103 pp. De Vries, D.A., 1963. Thermal properties of soils. In: W.R. van Wijk (Editor), Physics of Plant Environment. North-Holland, Amsterdam, pp. 210-233. Haneghem, I.A. van, 1981. Fen niet stationaire naaldmethode (warmtegeleiding, warmtecapaciteit, contactweerstand), Dissertation. Department of Physics, Wageningen Agricultural University, 187 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. Horton, R., 1982. Determination and use of soil thermal properties near the surface, Ph.D. Dissertation. New Mexico State University, Las Cruces, New Mexico, USA, 132 pp. Horton, R., Wierenga, P.J. and Nielsen, D.R., 1983. Evaluation of methods for determining the apparent thermal diffusivity of soil near the surface. Soil Sci. Soc. Am. J., 47: 25-32. Kimball, B.A. and Jackson, R.D., 1975. Soil heat flux determination: a null-alignment method. Agric. For. Meteorol., 15: 1-9. Nagpal, N.K. and Boersma, L., 1973. Air entrapment as a possible error in the use of a cylindrical heat probe. Soil Sci. Soc. Am. J., 37: 828-832. Riha, S.J., Mclnnes, K.J., Clids, S.W. and Campbell, G.S., 1980. A finite element calculation for determining thermal conductivity. Soil Sci. Soc. Am. J., 44: 1323-1325. Seemann, J., 1979. Measuring technology. In: J. Seemann et al. (Editors), Agrometeorology. Springer-Verlag, Berlin, pp. 40-45. Sene, K.J., 1994. Parameterisations for energy transfers from a sparse vine crop. Agric. For. Meteorol., 71: 1-18. Soet, M., Droogers, P., Jaarsma, M.N., Kim, C.P., Monincx, J.F. and Stricker, J.N.M., 1993. HAPEX-SaheI: Basic description of methods and datasets, Rapport 43. Vakgroep Waterhuishouding, Wageningen, The Netherlands, 50 pp. Tanner, C.B., 1963. Basic instrumentation and measurements for plant environment and micrometeorolgy, Soil Bull. 6. University of Wisconsin, Madison, WI. Ten Berge, H.F.M., 1990. Heat and water transfer in bare topsoil and the lower atmosphere, Sire. Monogr. 33. Pudoc, Wageningen, The Netherlands, 207 pp. Van Loon, W.K.P., 1991. Heat and mass transfer in frozen porous media, Ph.D. Thesis. Wageningen Agricultural University, Wageningen, The Netherlands, 204 pp. Wijk, W.R., van, 1963. Physics of plant environment. North-Holland, Amsterdam, 382 pp.