Soil heat flux measurements in an open forest

Phys. Chem. Earth, Vol. 21, No. 3, pp. 101-105, 1996. © 1997 Elsevier Science Ltd All fights reserved. Printed in Great Britain 0079-1946/96 $15.00 + 0.00 PII: S0079-1946(97)00018-9

Soil Heat Flux Measurements in an Open Forest M. W. J. van der Meulen and W. Klaassen* University of Groningen, Department of Physical Geography, Kerklaan 30, 9751 NN Harem The Netherlands

Received 28 October 1996; accepted 27 November 1996 Abstract

radiation above the canopy, in more open forests, the soil heat flux will be considerably larger. The aim of this experiment was to determine the soil surface heat flux (Go) accurately, and to compare it with the net radiation above the canopy (R~). This relation is expected to depend on L. Since the extinction of radiation in canopies is approximately exponential in L, we examine an exponential relation between Go / R, and L. Four comparable studies wiU be included in this relationship.

The soil surface heat flux in an open oak forest was determined at four locations to ac~unt for the heterogeneity of the forest. Soil temperatures and soil water content were measured at several depths and an integration method with three layers was used. The thickness of the bottom layer was determined with a spectral method. The soil surface heat flux was compared with the net radiation above the canopy for four typical days in 1995. These data were fitted linearly. The slope of this parameterisation was 0.092, with a leaf area index of 2.5 (fully-leafed canopy). This result was compared with four other studies. To produce an exponential fit of the slope against the leaf area index the Beer-Bouguer law for radiation extinction in canopies and a soil surface heat flux proportional to the net radiation at the forest floor was used. An extinction coefficient of 0.36 was found. This result is recommended for future studies, if soil surface heat flux is requested and net radiation data above the canopy as well as leaf area index are available. © 1997 Elsevier Science Ltd. 1. Introduction

2. Theory

2.1 Integration method An integration method was used to determine the soil heat flux in an open oak (Quercus robur) forest. This method is considered to be the most robust method to calculate the soil heat flux (Bink, 1996). It adds up the net soft heat storage in the different soil layers. By assuming that the soil heat flux is zero below a certain depth, the total net heat storage of the soil layers equals the soil surface heat flux Go [Win'2]: Go = (C/At) Z~Az~ATi

The soil surface heat flux is often considered to be an unimportant component of the anergy balance of a forest. However, in forests with a small leaf area index (L), as in the experiment described here, the soil surface heat flux can make up a si~ificant part of the energy balance. Whereas in dense forests the soil surface heat flux is only about 3-6% of the net

(I)

where C is the volumetric heat capacity [J m "3 K'Z], At the time interval (30 minutes) [s], i the soil layer number [-], A~ the thickness of layer i [m] and ATi the temperature change of layer i, during the time interval At [K]. Since we collected data from only three depths per location, we paid special attention to the layer discretisation. A spectral method was used to calculate the thickness of the bottom layer.

"Corresponding author

101

102

M.W.J. vail der Meulen and W. Klaassen

2.2. Determination of layer thicknesses A difficulty when using the integration method, is to choose the best layer thicknesses for an accurate determination of the soil surface heat flux. This problem was addressed using the spectral method (Koorevaar et al., 1983). It uses the daily amplitude of soil temperatures at several depths. These amplitudes A(z) roughly decrease exponentially with depth z (equation 2a). The characteristic length of this exponential decay is called the damping depth

(D). A(z) = Ao exp[-z/D]

(2a)

To determine the depth of the bottom of the third (lowest) layer, we used the exponential decay which is mentioned above. The thickness of this layer is such that:

2i=1.2,3 A(zi) Azi = Ao Jo~ exp[-z/D]dz

(2b)

TABLE 1: Conditions during the four days ("KNIVII", 1995). See paragraph shown are the coefficients "a" and average values were taken from Fig. Date

S

T

m 1995 27 Ma? Ig

P

swc

Max. R~

a

5 0

19

0

034

733

19

2.5

0.21

234

Jl~~ Au-

12

31

0

0.20

~66t Octo* bet Ave-

8.5

18

0

6.4

22

0.6

examined 4.1. Also "b". Their 4. b

RZ

.087

-13

0.92

.091

-3.6

0.59

567

.11

-15

0.92

0.18

390

.096

-4,7

0,86

0.23

481

.092

-8.4

0.83

rage:

with: S T

Sunshine duration [hours]. Maximum air temperature

[°Cl. P swc Max. R.

Precipitation [mm]. Soil water content [m3/m3]. Maximum net radiation above the canopy [Wm-2]. slope "a" [-]. offset "b" [Wm-2]. Correlation coefficient [-].

This equation states that in the graph of A(z) against z, the total area below the three discretisation rectangles is equal to the area below the exponential curve, integrated from the surface down to infinity.

a b R2

3. Location and experimental set-up

Soil heat fluxes were determined using four sets of temperature/moisture sensors which were placed in a square, with sides of roughly 10m. The square was located 25m south of a meteorological tower where the net radiation (short-wave and long-wave) above the canopy was measured. Soil temperatures were measured at depths of 5, 8 and l lcm Soil water content was measured at a depth of 8cm, using TDR and FDR techniques. (TDR/FDR: Time/Frequency Domain Reflectometry,)

3.1. Description of experimental site The experimental site was located in the Bankenbos near Veenhuizen in the north of the Netherlands (530 01'N, 60 25'E). It consisted of an oak (Quercus robur) patch of 370m x -150m. The patch was recently thinned, resulting in many openings in the canopy and a leaf area index between 2 and 3 during the fully-leafed period. The average tree height was 25.4m (Post, 1995). The soil at the four measurement sites consisted of humus rich sand down to 55cm deep. The organic matter was found mainly in the upper 5 cm. The average volumetric soil composition between a depth of 0 and 15 cm was 60% pores, 5% organic matter and 35% mineral matter. The thermal properties of the soil were taken from De Vries (1963). The soil moisture content is given in table 1.

3.2. Experimental set-up

4. Results and discussion

4.1. Soil surface heat flux The average value of the damping depth (D) at our experimental site in 1995 was 13cm. The variance of D was small (~2cm), which justified the use of a fixed value in equation 2b. The water content of the soil played a significant role (up to a factor of two) in the calculation of the soil surface heat flux, due to its influence on the volumetric heat capacity (C). Figures 1 and 2 show the soil heat flux at the surface (averaged over the four locations) against the Julian day in 1995. The maximum occurred at around 12:00 GMT, with a standard deviation of approximately two hours.

103

Soil Heat Flux Measurements in an Open Forest

The daily cycle was clearly distinguishable, except in Fig. 1, (16-18 November 1995).

~60 • &

140

. . . . . . =et2

r~

=I .I ~E

iil

40 ~

•

20.

!1

Wv( 321

321

27 Msy 1~95

322

Fig. 1. Soil surface heat flux. 16-18 November 1995. Solar radiation was small at that time of the year, and the daily cycle of the temperature was seriously disturbed by a cold front passage in the evening of 16 November ("KNMI", 1995). Whereas 16 November was rather warm (T,~w,~ = 8.5°C) and wet (10ram precipitation), 17 and 18 November were cold ( T , ~ - 2°C), and wet (especially the lg th, with 16ram precipitation), with some snowfall on both days. Fig. 2 shows a recurring pattern around noon, each day.

Fig. 3. Soil surface heat flux against time on 27 May 1995. The average horizontal variance of the soil surface heat flux however was much smaller. We believe that averaging the four sets reduces the effect of heterogeneity to an acceptable level. When examining the scatter plots (Fig. 4) of Go against 1~, the scatter in the value of Go had a range of 20Win "2. This provided confidence in the averaging of four sensor sets. 80 1 I

•

60 I

y = 0.0917x - 8.3575

•.

eo 20 4

80-

,.

~;o."

* * e,.~,.,,,"~

o

.

~..Iqie.

°i A

-1

i: i ?....I ;t 230

231

*-40

........

,~e ''D'~

"

~]dr:'/Jt.

• ~

"

~ 300

"

~

,

400

500

~ 600

700

; Net radiation [Wire2]

Fig. 4. Scatter plot of the soil surface heat flux against the net radiation above the canopy. Data of 27 May, 18 July, 19 August and 6 October 1995 were used.

232

Fig. 2. Soil surface heat flux. 18-20 August 1995.

4.2. Comparing soil surface heat flux with net radiation above canopy

This was a result of the tree configuration around the instrumental set-up casting shadows over the measuring point. For one set the flux was much larger (up to 150Wm2), caused by the absence of trees south of it, resulting in a prolonged period of direct sunshine on that spot. So, in extreme cases, this variability produced differences between locations of up to 100Win2 (Fig. 3).

The soil heat flux at the surface is often approximated by: Go = a R, + b

where "a" is a dimensionless parameter (slope) which depends on L, solar angle, soil water content and weather conditions (e.g. cloudiness) and "b" is an offset [Wm21, depending on the experimental site, the type of forest and soil, time of year, etc. Examining equation 3, it is obvious that slope "a" is positive, since an increasing R~ results in an increase of Go: dGo/dl~ > 0

PC£ ~I-3-B

(3)

~

"a" > 0

80~3

104

M. W. J. van der Meulen and W. Klzassen The net soil heat flux over one year is approximately zero, since the soil temperatures are roughly the same each year:

The extinction of radiation through a canopy is described by the Beer-Bouguer law (Rosenberg et al., 1983):


R~ = Rn exp [-~L]

The net radiation above the canopy however is positive over one year. Hence, offset "b" is negative:

13 is called the extinction coefficient. It is 0.30.5 for vertical leaves, and 0.7-1.0 for horizontal leaves (Rosenberg et al., 1983). Combining equations 4 and 5 produces:

(R,) > 0

~

(5)

"b" < 0 Go = ~ R~ exp[-13L]

Table 1 shows the environmental conditions and the resulting coefficients "a" and "b" for the four days in 1995 we examined. L was approximately 2.5 for all these days. These four days are selected to give a representative value of "a" and "b" during the fully-leafed period and are therefore used in the final parameterisation. For single days, the values of "a" and "b" showed considerable scatter. Averaging over a few days resulted in more reliable values of "a" and "b". Offset "b" could be estimated at -9Wm 2 , with a variance of 6Wm 2, which is small compared to the total error of Go.

(6)

Fig. 5 shows the exponential fit of the data. ~his resulted in the following values of the coefficients: ct = 0.23 and 13 -- 0.36. The value of 13 corresponds to the lower end of the range. A low value seems reasonable, since soil heat flux is also influenced by air temperature. ~, = 0.2303o "°z~ex R = = 0.903 I

.]

•

~o 0.1

i 4. 3. Relation between L and "a"

The relation between the value of "a" and the leaf area index of the forest during the fullyleafed period was investigated empirically by comparing our results to other studies. See table 2. TABLE 2: Summary of outcome of several comparable experiments. See paragraph 4.3. Exp.merit

Forest type

Com-

L

a

2.5

0.092

mcrdJ

Oak ment

Avetaft over four days in May, July, August and Octolaa" 1995

BMdocchi et al.

Oek-hickow

4.9

0.036

Ten I ~ e (1990) and Stull

"l~pical value for bare soib

Combined data

0

0.36

ltilz mid Lindroth (1996)

Short-rotation willow coppic~

0.2 2.0 4.0

0.15 0.095 0.06

V~.slra (1991)

//ax=l Coe=~ laraz and otk)

Only daily m~anum values of net radiation and soil heat flux were tilted May and Septemb~ 1990

5.4

0.037

Qgg4)

~19~

As a theoretical foundation we used: Go ~ c~l~

(4)

1L is the net radiation at the forest floor. We emphasise that equation 4 is an approximation.

0.01

0

1

2

3

4

5

L

Fig. 5. Slope "a" against leaf area index. The fit is exponential. Our experiment plus four other studies are plotted.

5. Conclusions We conclude that the soil surface heat flux can be estimated from the net radiation above the canopy with an accuracy of about 20Win -:. This relation was found to depend on L. Comparable to the Beer-Bouguer law, we used the exponential relation of equation 6. Our experiment combined with four other studies yielded: ct = 0.23 and [3 = 0.36.

Acknowledgements This work was supported by the Winand Staring Centre in Wageningen and the Department of Physical Geography of the University of Groningen. Jan-Willem van den Bar& Peter van Breugel, Jan van den Burg, Jan Delvigne, Jan Spieksma and Henk de Groot are gratefully acknowledged for their support.

6

Soil Heat Flux Measurements in an Open Forest References

Baldocchi, D.D., Matt, D.R., Hutchison, B.A. and McMillen, R.T., 1984. Solar radiation within an oak-hickory forest: an evaluation of the extinction coefficients for several radiation components during fully-leafed and leafless periods. Agric. For. Meteorol., 32: 307-322. Bink, N.J., 1996. The structure of the atmospheric surface layer subject to local advection. PhD thesis Wageningen Agricultural University, the Netherlands, 206p. De Vries, D.A., 1963. Thermal properties of soils. In: W.R. van Wijk (Editor), Physics of plant environment, North Holland, Amsterdam. Iritz, Z. and Lindroth, A., 1996. Energy partitioning in relation to leaf area development of short-rotation willow coppice. Agric. For. Meteorol., 81: 119-130. "KNMI", Royal Dutch Meteorological Institute, 1995. MOW-Bulletin. Maandoverzicht van het weer in Nederland, De Bilt, 92° jaargang. ISSN 167-8248.

Koorevaar, P., Menelik, G. and Dirksen, C., 1983. Elements of Soil Physics, Elsevier, Amsterdam. Post, M., 1995. Het bepalen van de Leaf Area Index in bossen. Report no. 39. Dept. Phys. Geogr., University of Groningen, the Netherlands. Rosenberg, N.J., Blad, B.L. and Verma, S.B., 1983. Microclimate: The Biological Environment (second edition). John Wiley & Sons, Inc, New York. Stull, R.B., 1988. An Introduction to Boundary Layer Meteorology. Kluwer Academic Publishers, Dordrecht, the Netherlands. Ten Berge, H.F.M., 1990. Heat and water transfer in bare topsoil and the lower atmosphere. Simulation Monographs 33, Pudoe Wageningen, the Netherlands, 207p. Veenstra, D., 1991. Modellering van bodemwarmtefluxen met behulp van dagelijkse weergegevens. Internal report. Dept. Phys. Geogr., University of Groningen, the Netherlands.

105