Thermal roughness length of a boreal forest

Agricultural and Forest Meteorology 98±99 (1999) 659±670

Thermal roughness length of a boreal forest Meelis MoÈldera,*, Anders Lindrothb a

Department of Earth Sciences/Hydrology, Uppsala University, VillavaÈgen 16, SE-752 36 Uppsala, Sweden b Department for Production Ecology, Faculty of Forestry, SLU, Box 7042, SE-750 07, Uppsala, Sweden

Abstract The aim of this study was to determine the roughness length for temperature (zot), which has rarely been done for forests. The analysis was based on measurements of pro®les of wind speed, air temperature, and surface radiation temperature in a forest at the NOPEX Central Tower Site, 30 km north of Uppsala, Sweden. This site represented a mixed pine and spruce forest with a height of about 24.5 m. The analysis of the pro®les took into account the roughness sublayer corrections. A single displacement height, equal to 21.1 m, was applied for both momentum and heat exchange. The roughness length for wind speed (zou) was found to be 1.75 m. The surface radiation temperature was measured with a ®xed and a moving sensor and was studied in detail. It was found that the inhomogeneities of the forest introduced large variations in the surface radiation temperature (up to 5 K). The temperature from the ®xed sensor pointing under 458 to the east was close to the average taken over all measured directions, near noon. Using the near-noon ®xed-sensor data and assuming that it best represents the effective surface temperature, the quantity ln(zou/zot) was found to be slightly negative (ˆÿ0.5) which implies that the roughness length for temperature is larger than that for wind speed. This is quite an unexpected result but it can be explained in terms of a deep roughness sublayer above the canopy, where heat transfer is enhanced compared to momentum transfer, and to the fact that the main roughness elements, small sized needles, have a thin boundary layer and therefore a small bluff-body effect. The analysis covered day-time unstable conditions only. # 1999 Elsevier Science B.V. All rights reserved. Keywords: Pro®le measurements; Roughness sublayer; Turbulent ¯uxes; Surface radiation temperature; Excess resistance; Pinus sylvestris; Picea abies

1. Introduction Most climate models are very sensitive to the exchange of heat and water at the boundary between the earth's surface and the atmosphere (Garratt, 1993). An erroneous partitioning of the available energy will inevitably lead to an erroneous estimation of tempera*

Corresponding author. Present address: Department of Physical Geography, Lund University P.O. Box 118, SE-22100 Lund, Sweden.

ture and humidity development in the planetary boundary layer. An accurate parameterisation of the exchange processes near the surface is therefore of vital importance. Boreal forests, in spite of their importance for the global hydrological and biogeochemical cycles (Thomas and Rowntree, 1992), have rarely been studied in this context mainly because of the large practical dif®culties involved in such studies. For parameterisation of exchange processes at the surface, the concept of roughness lengths has become a simple and useful tool (e.g., Brutsaert, 1982) widely

0168-1923/99/$ ± see front matter # 1999 Elsevier Science B.V. All rights reserved. PII: S 0 1 6 8 - 1 9 2 3 ( 9 9 ) 0 0 1 3 2 - X

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M. MoÈlder, A. Lindroth / Agricultural and Forest Meteorology 98±99 (1999) 659±670

used in models and other calculation schemes. According to the de®nition, the roughness lengths for wind speed (zou) and temperature (zot) can be determined by extrapolating wind and temperature pro®les from the fully turbulent layer down to the zero and the surface temperature value, respectively. Relation between the two roughness lengths is often expressed through kBÿ1 ˆ ln(zou/zot) which is related to the so-called excess resistance. Correct values of zou, zot or kBÿ1 have also great importance in application of remote sensing techniques for determination of surface ¯uxes. There is a number of examples where the quantity kBÿ1 has been determined for crops and other types of low vegetation, for instance, for short grass (Duynkerke, 1992); bare soil, low and medium grass, bean crop, savannah scrub (Garratt and Francey, 1978); soybean and sorghum (Heilman and Kanemasu, 1976); wheat stubble (Hicks et al., 1986); mixture of grass and stones (Kohsiek et al., 1993); pasture (Kubota and Sugita, 1994); arid area with mixture of bushes and bare soil, wheat (Kustas et al., 1989); barley (MoÈlder, 1997); prairie grass (Stewart, 1995); eight semiarid areas with grass, scrubs, and low trees (Stewart et al., 1994); fallow savannah and millet (Trou¯eau et al., 1997); semiarid vineyard, fallow savannah, and bare soil (Verhoef et al., 1997). In the case of forests, the canopy is little heated/ cooled relative to the air, and the temperature gradients in the air are very small. Accordingly, there are high requirements on the measurement accuracy for both surface temperature and gradients and therefore, the temperature roughness for forests has rarely been determined experimentally. The review of Garratt and Hicks (1973) refers to two cases representing coniferous (pine) forests: Stewart and Thom (1973) and Hicks et al. (1975). In fact, Stewart and Thom (1973) did not obtain their result on kBÿ1 from the measurements, but used semi-theoretical deductions of Thom (1972) instead. Hicks et al. (1975) did calculate the value of the temperature roughness from the measurements, but the `surface' temperature was not a real surface temperature but the air temperature measured within the canopy, 1.5 m from the ground. However, these estimates showed that zou and zot were quite close to each other, ln(zou/zot) being approximately 1. More recent results concerning a pine forest have been obtained in the HAPEX-MOBILHY experiment.

Jacquemin and Noilhan (1990) used the assumption zou ˆ zot for modelling purposes and the results were well veri®ed by the tower measurements. A contrasting result was found by Mahrt and Ek (1993) who deduced from aircraft measurements that zot was 5  103 times smaller than zou. It should be noted that the forest under study was quite heterogeneous, containing some 35% of clearings. The sensible heat ¯ux and the surface temperature obtained from a boundary layer simulation by Holtslag and Ek (1996) ®tted best with the aircraft measurements using Mahrt and Ek (1993) ®nding. Holtslag and Ek (1996) admit that the same calculations with zou ˆ zot agreed better with the tower measurements, but then the simulated boundary layer development was in error. They conclude that the tower measurements together with zou ˆ zot represent a scale of 1 km, but the aircraft ¯uxes and zou ˆ zot/5  103 are appropriate for scales of 10 km and more. Nowadays, the surface temperature is usually measured radiometrically using infrared thermometers (IRT). Such thermometers have different viewing angles, spectral response etc. and they can be oriented in different angles with respect to the surface and the sun beams. It is, therefore, still an open question how the surface temperature, that is most relevant for heat exchange and, accordingly, for roughness length estimates, should be determined. The angular variation of the surface radiation temperature has quite well been studied for low canopies (e.g., Huband and Monteith, 1986; Lagouarde et al., 1995) but information from forests is more scarce. Lorenz and Baumgartner (1970) showed that the temperature of the sunlit and shaded sides of a spruce stand can deviate by as much as 2.5±3 K. Similar results were obtained by Sun and Mahrt (1995) in the BOREAS experiment: the temperature of a spruce stand varied by about 2 K depending whether a sunlit or shaded side was observed. They also found that the soil temperature beneath the canopy varied strongly and the composite radiation temperature measured in nadir was cooler than the air temperature above the forest and this created serious problems for thermal roughness length estimations. It can be seen from the examples above that there are large uncertainties in the ln(zou/zot) estimates for forests. The main aim of this paper is to provide a good estimate of this parameter for a boreal forest. An

M. MoÈlder, A. Lindroth / Agricultural and Forest Meteorology 98±99 (1999) 659±670

advantage of this study is that the measurements were made in a tall (102 m) tower providing accurate information on the surface layer pro®les and that the roughness sublayer effects were studied and quanti®ed in advance (MoÈlder et al., 1999a). 2. Material 2.1. Measurement site and period All measurements used in this analysis were made at the NOPEX Central Tower Site in Norunda, central Sweden (Grelle and Lindroth, 1999; MoÈlder et al., 1999b). This site was situated ca. 30 km north of Uppsala (60850 N, 178290 E; alt. 45 m), and consisted of mixed pine and spruce stands with an age range of 50±100 years growing on a boulder rich till. The measurement tower was surrounded by a 100 years old mixed spruce-pine stand of a maximum height of 24.5 m. The leaf/needle area index in the stands closest to the tower was in the range 4±6. The vegetation of the forest ¯oor consisted mainly of mosses and dwarf shrubs. In general, a homogeneous forest extended 1.5±6 km from the tower. Different measurements have been carried out during different periods. The period for the roughness length analysis, from 29 June to 31 July 1995, was mainly selected because of good pro®le measurements at that time. It also coincided with the period used for determination of the roughness-sublayer corrections (MoÈlder et al., 1999a). The Swedish local summer time is used throughout the paper, 13:10 hours is the actual solar noon. The ®rst half of the main measurement period was very dry, there were a few mm of precipitation on two nights. A heavy rain (16 mm) occurred on 17 July, some nights before and after this date contributed with a few mm too. Speci®c humidity was rather low, 4± 11 g kgÿ1. Midday net radiation values ranged from 400±650 W mÿ2, a large portion of this, up to 400 W mÿ2, was consumed by the sensible heat ¯ux. Maximum air temperature was on the warmest days between 19 and 278C. Wind speed was 2±4 m sÿ1 at the lowest, 28 m, level but could reach 4±11 m sÿ1 at the highest, 87.5 m, level. The dominant wind direction was south-western which was favourable in respect of fetch requirements.

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2.2. Profile measurements Wind speed was measured with two-dimensional (horizontal velocity and direction) sonic anemometers (Solent basic anemometer; Gill Instruments, Lymington, UK). The sensors were calibrated in a wind tunnel and the accuracy was estimated to be within 0.2 m sÿ1. Air temperature was measured by copper±constantan thermocouples relative to the highest measurement level (100.6 m), where the absolute measurement was made. The sensors were placed in ventilated double radiation shields. More details can be found in MoÈlder et al. (1999a, 2000). The measurement accuracy of temperature differences was tested against a Thermometer Interchange System and was estimated to be 0.03 K (MoÈlder et al., 2000). Temperatures from the following measurement levels: 24.5, 28, 31.7, 36.9, 43.8, 58.5, 73, and 87.5 m were used in this analyses. Anemometers were available only at ®ve heights: 28, 36.9, 43.8, 58.5, and 87.5 m. 2.3. Radiation temperature measurements Radiation temperature was measured by two IRTs (model 4000; Everest Interscience, Fullerton, USA). Both of them work in the 8±14 mm spectral band but have different ®eld of view: 4 and 158. Their speci®ed accuracy is 0.5 K. The 158-sensor was used as a ®xed sensor at the top of the tower (102 m height). It was pointing at 458 from the nadir to the east, and it was operating throughout the observation period. The forest it was looking at was the most uniform part of the forest around the tower. The signals from the anemometers and thermometers, and the ®xed IRT were measured and stored on a Campbell data-logger (CR-10; Campbell, Leicestershire, UK). The 48-sensor was mounted on a Pan Tilt Head (660 series; Videmech Limited, Hartley Wintney, UK). The Pan Tilt Head is originally designed to carry and accurately control CCD cameras. The Pan Tilt unit together with the Everest sensor were mounted on a boom, 2.5 m from the tower at 95 m height. The Pan Tilt Head was controlled by a separate data-logger (CR-10; Campbell, Leicestershire, UK), the program was supplied by In Situ Instrument (Ockelbo, Sweden). Measurements were performed at nadir angles 0±808 in 48 steps at three azimuth positions: (1) in the sun's principal plane along the sun beam, (2) perpen-

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Table 1 Ellipse-shape footprint geometry of the IRTs (m) Inclination angle (8)

Distance to the centre of the ellipse

The fixed sensor 45 77.0 The Pan Tilt-mounted sensor 0 0 20 25.5 45 70.0 60 121.2 80 397.0

Length of the ellipse

the accuracy was still within 0.5 K as speci®ed by the manufacturer. Width of the ellipse

41.3

28.7

4.9 5.6 9.8 19.7 168.8

4.9 5.2 6.9 9.8 28.2

dicularly, to the right of the ®rst azimuth direction, (3) in the sun's principal plane again, but against the sun beam. The resulting temperatures will be referred as along, across and against, respectively. One full measurement cycle covering all angles took about 4.5 min. These measurement were made from 11 May to 14 July 1995. The Pan Tilt unit cannot rotate 3608 because it has a so-called dead sector between 320± 3608. The unit was mounted so that the tower fell into this dead sector. When the sensor was in the border position of the dead sector, it could see partly the tower or the boom that was holding it. This could happen at 05:00±08:00 hours for the along temperature, 23:00± 02:00 hours for the across temperature and 17:00± 20:00 hours for the against temperature. The footprint of the ®xed sensor covered ®ve to eight trees and it should, thus, provide a good average value (Table 1). The moving sensor could see single trees at small nadir angles, but at angles over 408 it saw typically more than two trees. At large nadir angles, the footprint represented a very narrow `ellipse' and other stands longer away were within the ®eld view. The IRTs were calibrated before and after the measurement campaign against a black-body unit (Reemann's design; Tartu, Estonia). The sensor was kept at the room temperature and the black-body temperature was changed gradually up to 458C. The ®xed temperature sensor showed an excellent behaviour, deviations were within 0.2±0.3 K for the whole temperature range. The calibration of this particular sensor has turned out to be very stable for several years. The 48-sensor deviated at high black-body temperatures by ca. 1 K, but such high sensor-target temperature differences do not occur in the nature and

2.4. Sensible heat fluxes by eddy correlation measurements The sensible heat ¯ux from the forest was measured by eddy correlation systems placed on the tower at 35 and 70 m above ground. The wind components were measured by sonic anemometers (Solent 1012R2; Gill Instruments, Lymington, UK) placed on booms which extended ca. 5 m from the tower. Temperature ¯uctuations were measured with fast-response platinum-wire resistance thermometers. The system and software are described in detail by Grelle (1997). 3. Theory According to the atmospheric surface layer similarity theory, the pro®les of wind speed u and potential temperature  can be expressed by the following wellknown equations (Brutsaert, 1982; Garratt, 1992):   k z u ˆ ln (1) ÿ…Cu …&†ÿCu …&ou †† u zou   k z z ÿ…Ct …&†ÿCt …&ot †† with  ˆ …ÿs † ˆ ln T zot L (2) where u* is the friction velocity, T* is the temperature scale, z is height from the displacement height d, L is the Obukhov length, k ˆ 0.4 is the Karman constant, s is the surface temperature, zou and zot are the roughness lengths for wind speed and temperature, respectively, Cu and Ct are universal stability correction functions. The Obukhov length is defined as: Lˆ

u2 k…g=T†T

(3)

where g is the acceleration of gravity. Within the roughness sublayer, however, these equations have to be replaced by the following corrected ones (Physick and Garratt, 1995; MoÈlder et al., 1999a):   Z z k z dz Fu …1ÿu † ÿ…Cu …&†ÿCu …&ou ††‡ u ˆ ln u zou z z (4)

M. MoÈlder, A. Lindroth / Agricultural and Forest Meteorology 98±99 (1999) 659±670

…ÿs †

  k z ˆ ln ÿ…Ct …&†ÿCt …&ot †† T zot Z z dz Ft …1ÿt † ‡ z z

(5)

where Fu and Ft are universal non-dimensional gradients and u and t are the roughness-sublayer correction functions and z* is the roughness-sublayer height. These profiles contain the classical logarithmic and stability correction terms as Eqs. (1) and (2), but additionally new integral terms. The non-dimensional gradients in unstable conditions are used in the form given by HoÈgstroÈm (1988): Fu ˆ …1ÿ19:3&†ÿ1=4

(6)

Ft ˆ …1ÿ12&†ÿ1=2

(7)

The form of the gradient functions Cu and Ct can be found in Brutsaert (1982) or Garratt (1992). The following correction functional have been suggested by Cellier and Brunet (1992):  n z (8) u ˆ z z (9) t ˆ z This form was confirmed by MoÈlder et al. (1999a) where also the wanted numerical values were determined as: n ˆ 0.6, z* ˆ 23.9 m for wind speed and z* ˆ 35.9 m for temperature and humidity. 4. Data processing The value of the displacement height, 21.1 m, was determined in the previous study by MoÈlder et al. (1999a). This value gave the best agreement between two friction velocities, from pro®les above the roughness sublayer and from eddy correlation measurements. The measured pro®les of wind speed and air temperature from 24.5 up to 87.5 m were ®tted with Eqs. (4) and (5). The roughness length zou was found by extrapolating Eq. (1) to the zero value. In the next step, the measured pro®les of wind speed and air temperature were ®tted with Eqs. (4) and (5) again, using the ®xed mean zou value in the calculations. A direct evaluation of zot from Eq. (2), pro®le by pro®le, is not recommended because it is very sensi-

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tive to errors. Eq. (2) can be re-written for z ˆ zou as:   k zou …o ÿs † ˆ ln ÿ…Ct …&ou †ÿCt …&ot †† zot T where o is a fictitious temperature called the aerodynamic surface temperature. This equation suggests that the slope of a plot of the temperature difference o ÿ s versus the scale T*/k equals to the mean ln(zou/ zot) if the stratification correction terms are neglected. In the next step, using the first estimate of ln(zou/zot), the correction terms can be lumped into o and a new estimate for ln(zou/zot) can be obtained. This iteration procedure must be continued until ln(zou/zot) converges. The analysis was restricted to day time only, de®ned by positive net radiation. Those pro®les where wind could blow through the tower were excluded from the analysis. The zot analysis was additionally restricted to positive sensible heat ¯uxes. 5. Results and discussion 5.1. Typical profiles of wind speed and air temperature Traditional semi-logarithmic pro®les of wind speed and potential air temperature (Eqs. (1) and (2)) do not follow the actual pro®les down to the canopy top (Fig. 1). Deviations start to appear on average at 45 and 57 m for wind and temperature pro®les, respectively. This is the top of the so-called roughness sublayer. The roughness sublayer effects act in making the gradients very small, which is especially critical in respect of accurate measurements of temperature pro®les. The distribution of differences in potential temperature over the full height interval, the roughness sublayer, and the layer above the roughness sublayer are presented in MoÈlder et al. (2000). The potential temperature differences over the full height interval and the roughness sublayer reach 0.7±0.8 and 0.5± 0.6 K, respectively. The differences over the layer above the roughness sublayer are small, only about 0.2 K. Therefore, all measurement levels should be used in combination with modi®ed pro®le functions (Eqs. (4) and (5)) to determine the turbulent scales u* and T*. The surface temperature exceeds the air

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Fig. 2. Daily means and standard deviations of the roughness length for wind speed.

Fig. 1. Example of one vertical wind-speed and air-temperature profile on 28 July 1995 at 15:00 hours. Filled symbols are measured data and curves are traditional semi-logarithmic profiles. Note that typically o exceeds s.

temperature near the tree tops by 1.5 K in maximum. The surface temperature may be lower than the aerodynamic temperature, o. The air temperature within the stand is rather constant or slightly decreasing with height (Fig. 1). 5.2. The roughness length of wind speed The thermal roughness length is usually expressed as a fraction of the roughness length for wind speed. Alternatively, the surface temperature is related to the aerodynamic temperature, o, i.e. the extrapolated air temperature at zou height. Therefore, the roughness length for wind had to be determined before proceeding to the determination of the roughness length for temperature. Daily mean values of the roughness length for wind speed show quite constant value (Fig. 2) except for 3 days which give considerably lower values. These 3 days are characterised by low wind speeds, but on other hand, the same low wind speeds occurred also on some other days but the roughness length was still close to the over-all mean. One difference in conditions for these 3 days was that it was raining, and these data are, therefore, considered to be less reliable. Mean zou over all days is

1.65 m, but excluding the 3 less-reliable days gives a value of 1.75 m. The latter value is used in the subsequent analysis. Note that the remaining small variations can neither be explained by the wind direction nor by the wind speed. The quotient of the zou value to the stand height is 0.07 which is in a good agreement with the previous data (Jarvis et al., 1976; Wieringa, 1993). 5.3. Directional variation in surface radiation temperature The angular dependence of the radiation temperature showed consistent behaviour during different sunny days, and therefore the temporal development during a selected day can be used as a representative sample (Fig. 3). It is dif®cult to draw any conclusions about the temperatures measured near the nadir direction (hatched areas) because trees were taken down close to the tower and the sensor could see the ground and the constructions around the tower. The across and against temperatures are close to each other, the against one being slightly lower. The along temperature, disregarding the peaks, tends to be higher by 1 K than the two others after 10:00 hours. This difference could be up to 2 K on other days. The positive peaks in the along temperature some hours before and after the noon are caused by some openings in the forest (a small road and a larger gap in the canopy). The sensor could not directly see the ground surface itself, but it saw the sides of the trees, which were not shaded by any neighbouring tress, and accordingly, these trees were strongly heated by the sun. Similar negative peaks in the against temperature at 16:00 hours are caused by the sensor seeing a swampy patch in the

M. MoÈlder, A. Lindroth / Agricultural and Forest Meteorology 98±99 (1999) 659±670

Fig. 3. Angular variations of the surface radiation temperature measured by the Pan Tilt-mounted sensor at different times on 24 June 1995: stars Ð the along temperature, filled circles Ð the against temperature, open squares Ð the across temperature. The hatched areas show where the sensor could see the ground and the constructions around the tower.

south-western direction. Sometimes the treeless stripes making free space for the stay wires holding the tower also caused `unexpected' peaks in the radiation temperature. It can be learned from this experience that undisturbed homogeneous-forest curves are very dif®cult to measure in the real nature. The exact relationship between the three temperatures varied from day to day depending on many factors and it could not be described by a simple mathematical formula. It should be remembered that the sensor did not see exactly the same stand at large nadir angles (see Table 1). Nothing is known about temperature variations between stands. One problem with IRT determinations of surface temperature for a complex structure such as a forest

665

canopy is its representativeness. If the canopy is very open, the sensor will see illuminated and shaded spots at the ground, which might have much different temperatures than the canopy and therefore `bias' the mean surface temperature. The `correct' mean surface temperature in this context is the one that gives rise to the `true' sensible heat ¯ux from the area seen by the sensor. We know for instance that the heat transfer is much more ef®cient at the top of the canopy than at the ground. This means that a spot of a certain temperature actually should be given a weight depending on the heat transport resistances from that spot to some reference level above the canopy. Apparently, a spot of a certain view angle at the ground should be given another weight compared to a spot of similar view angle high up in the canopy. On the other hand, it is dif®cult to conceive any other method, which could be better than IR thermometry in measuring the mean surface temperature of a forest. In order to assess this problem, the gap probability of the canopy was measured on several occasions. It was determined using an IRT with 48 ®eld of view looking at 0, 20, and 458 zenith angles. The maximum gap probability was 0.35 at 08 and it decreased to 0.1 at 458 nadir angle. Measurements of ground surface temperature with the same IRT showed that illuminated spots could be typically 5±8 K above stand air temperatures. Now, the energy emitted in a certain spectral range was estimated as a power function of the absolute temperature (e.g., Svendsen et al., 1990), and using a simple two-layer (canopy and ground) approach, it could easily be shown that the difference between the composite temperature and the canopy temperature was in the range 0.5±0.1 K for nadir angles from 0 to 458. Thus, we can conclude that the effect of ground-surface temperature is relatively small even at nadir angles below 458. However, to include in some extent the effect of the ground, it was decided to construct an effective surface temperature by averaging the measured temperatures over the nadir angles from 20 to 808 and over all available azimuth directions. The averaged Pan Tilt temperatures relative to the ®xed-sensor temperature show a typical daily pattern (Fig. 4). Some features discovered already in Fig. 3 appear even more clearly here. During night, all temperatures are relatively close to each other. During daytime, the against temperature is about 0.5 K lower

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M. MoÈlder, A. Lindroth / Agricultural and Forest Meteorology 98±99 (1999) 659±670

Fig. 4. A diurnal pattern of the averaged (20±808 from nadir) Pan Tilt-measured temperatures relative to the fixed-sensor temperature on 29 May 1995: stars Ð the along temperature, filled circles Ð the against temperature, open squares Ð the across temperature, the line Ð the mean over the three temperatures where the across temperature was given a double weight. The hatched areas correspond to the periods when the Pan Tilt unit was stopped at the border of the dead sector and the IRT could see some constructional elements of the tower.

than the across temperature. The along temperature is 2 K higher than the against one. The mean over the four principal azimuths is closest to the across temperature, and it changes sign from positive to negative at about 14:00 hours (1 h after the solar noon which occurs at 13:10 hours). The ®xed sensor acts as an against sensor in the mornings and as an along sensor in the evenings. The ®xed-sensor temperature represents well the mean temperature at and near noon (it acts as an across sensor then). 5.4. The radiometric roughness length of temperature The surface radiation temperature is used for the surface temperature without any corrections for the emissivity and the re¯ected long-wave sky radiation and, therefore, the obtained roughness length for temperature should be called radiometric. Plotting o ÿ s versus the T*/k (Fig. 5a) using the ®xed-sensor temperature near the noon-time, where it can be considered to represent a mean stand temperature, results in a line with the slope of ÿ0.422. As the points converge close to a line, it is clear that no dependence on the roughness Reynolds number Reo is observed, and this forest can be characterised by a

Fig. 5. The temperature difference o ÿ s versus the scale T*/k: (a) the fixed-sensor temperature near noon is taken as the effective s, (b) the along temperature is taken as the effective s.

single zot value. An iteration gives that ln(zou/ zot) ˆ ÿ0.503. The negative value, implying a higher temperature roughness than wind roughness, is quite an exceptional result at ®rst glance. Using the along temperature instead of the ®xed one demonstrates a higher scatter, but with a clear conclusion that zou ˆ zot (Fig. 5b). This result seems to be more logical, i.e., the roughness length for temperature is not larger than that for wind. Accepting this means that the temperature of the sunlit tree sides is most appropriate for heat exchange. From practical point of view, this temperature is more dif®cultly determined and additional unwanted variations due to the forest's inhomogeneities are introduced. 5.5. Possible corrections of the radiation temperature The magnitude of the atmospheric correction due to water vapour was calculated for an extreme case: low wind (u* ˆ 0.5 m sÿ1) and large temperature gradient (sensible heat ¯ux: H ˆ 300 W mÿ2). Speci®c humidity was set to a typical value of 7 g kgÿ1 near the canopy and its pro®le corresponded to a latent heat ¯ux of 300 W mÿ2. The stand temperature exceeded the air temperature by 1.5 K. The air layer between

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24.5 and 95 m was split into 0.5 m layers. The simple calculation procedure given in Paltridge and Platt (1976) was used. The transmissivities were calculated according to Feigelson (1970) where the needed coef®cients in the 8±14.3 mm band were tabulated in small wavelength intervals. The increase of the nadir angle resulted in corresponding increase of the optical depth of water vapour. The calculations resulted in 0.03, 0.045, and 0.149 K correction for nadir, 45 and 808 nadir angles, respectively. These values are negligible compared with other possible errors. Information on the emissivity of coniferous forests is scarce. Arp and Phinney (1980) give values of 0.97± 0.99 in the 10.5±12.5 mm band for different pine species. Salisbury and D'Aria (1992) report that pine needles have a high (about 0.98) and uniform emissivity over the 8±14 mm spectral band. The emissivity of tree bark may slightly be lower according to them. The emissivity of a stand is remarkably increased because of the cavity effect. Besides, the emissivity of a stand depends on the viewing direction. In situ measurements of stand emissivities are extremely dif®cult. Rubio et al. (1997) found that trees have on an average an emissivity of 0.983, in particular, a value of 0.982 was presented for a pine forest. It seems to be more reliable to rely on model calculations of canopy emissivities (Anton and Ross, 1990; Franc,ois et al., 1997). Both models suggest an emissivity higher than 0.99 for a leaf area index of 6. The model of Anton and Ross (1990) prescribes an emissivity of 0.95 for both leaves and soil. The model of Franc,ois et al. (1997) gives 0.98 for leaves and 0.94 for soil. The emissivity of needles is probably 0.98 indeed, but the ground surface beneath a stand is usually covered with an understory, which has remarkably higher emissivity than soils. In summary we may assume a mean emissivity of our stand to be about 0.995. This emissivity correction is typically below 0.3 K and would change the results shown in Fig. 5a slightly in the direction of similarity between zou and zot. 5.6. Discussion on the negative ln(zou/zot) value The quantity ln(zou/zot) is related to the non-dimensional excess resistance kBÿ1 which expresses the difference between heat and momentum resistances over the entire roughness sublayer. For simplicity we

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do not consider the strati®cation effects here. According to Thom (1972) and Stewart and Thom (1973), the excess resistance consists of two terms: an `individual element' or `bluff-body' contribution and a `canopy¯ow' contribution. An extensive roughness sublayer has been detected over our forest; hence, a roughnesssublayer' contribution must be added to the 'canopy¯ow' contribution. The heat exchange is more ef®cient than the momentum exchange in the roughness sublayer (up to 57 m) (MoÈlder et al., 1999a) which causes the resistance to heat exchange over the entire roughness layer to be lower as compared with that for momentum. This makes the `roughness-sublayer' contribution to be about half of the value of ÿ0.5 that was found. The other half is contributed by the `bluffbody' and real `canopy-¯ow' effects together but we are not able to separate them. The `bluff-body' contribution must be positive and very small, however. Brutsaert (1982), Jensen and Hummelshùj (1995), and McNaughton and van den Hurk (1995) present models which all predict the characteristic size of leaves/ needles to be an important parameter in the heat exchange parameterisation. In the present case, the size of the needles, a few mm, means that only a thin boundary layer can develop on them (see also Mahrt et al., 1997). With a thin boundary layer, the sensible heat ¯ux can be maintained large although the temperature difference needle-air is still small. The models of Brutsaert (1982), Jensen and Hummelshùj (1995), and McNaughton and van den Hurk (1995) predict values of 1.08, 0.50, and ÿ0.47 (u* ˆ 0.6 m sÿ1, characteristic needle size, Lf ˆ 1 mm) for kBÿ1, respectively. It should be mentioned that the ®rst two models assume logarithmic pro®les right above a canopy and may therefore give overestimated kBÿ1 values. McNaughton and van den Hurk (1995) value is very close to ours. 5.7. Comparison of sensible heat fluxes It is of great interest to deduce turbulent ¯uxes from one-level measurements of wind speed and air temperature and radiometrically determined surface temperature because it provides a link to remote sensing. We chose to use wind speeds and air temperatures from 87.5 m level and evaluated the prospects of the ®xed-sensor radiation temperature to estimate the sensible heat ¯ux. For this purpose the Eqs. (1) and

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Fig. 6. Calculated friction velocity (a) and sensible heat flux (b, c, d) versus the sonic measurements during a 1-month period.

(2) were solved iteratively using the ®xed parameters d ˆ 21.1 m, zou ˆ 1.75 m and zot ˆ zou/exp(ÿ0.5). The plot of calculated u* and H values against the eddy correlation values shows quite high scatter (Fig. 6a and b). The scatter in the u* plot is uniform over the full range of friction velocities while the scatter of H gets larger while it increases. Note that part of the H scatter is caused by the scatter in u*. In general, the points of sensible heat ¯ux, especially with higher H values, lie on the 1 : 1 line but with a tendency to slight

underestimation at smaller values. Fig. 6c and d demonstrate that other assumptions, i.e. ln(zou/zot) ˆ 0 and 2, give clear deviations from the 1 : 1 line. This again gives support for the values of ln(zou/ zot) ˆ ÿ0.5. Taking a closer look at Fig. 6b reveals that actually more points are found below the 1 : 1 line. In many days during the ®rst half of the day, the ®xed-sensor temperature is below the mean surface temperature and the sensible heat ¯ux H is underestimated (Fig. 7). The underestimation during morning hours may be of the order of 100 W mÿ2. The better ®tting data in Fig. 7 (blank cubes) are adopted from MoÈlder et al. (1999a) where all available pro®le data (eight levels for air temperature and ®ve levels for wind speed) and the Eqs. (3)±(9) were used in the calculations. 6. Conclusions

Fig. 7. Diurnal curves of the sensible heat flux on 27 and 28 July 1995: fat line Ð sonic measurements, filled circles Ð calculations with surface radiation temperature and one profile level, open squares Ð calculations with all available profile levels (from MoÈlder et al., 1999a).

Measurements of the directional surface radiation temperature are dif®cult to carry out from a tower because inhomogeneities of the forest introduce large variations at the same time as the averaging is poor.

M. MoÈlder, A. Lindroth / Agricultural and Forest Meteorology 98±99 (1999) 659±670

If a detailed investigation is to be made, other approaches should be preferred such as using a sensor travelling on a rope between two towers or a sensor mounted on an airborne platform. The best usage of a Pan Tilt-mounted sensor is to run it at a ®xed zenith angle (40±608) over the full range of azimuths and then form a mean value over all azimuth angles. Measurements and calculations indicate that the radiation temperature is weakly dependent on the nadir angle, but more strongly on the azimuth. The sunlit tree tops are 1±2 K warmer than the shaded ones. The mean surface radiation temperature measured and averaged over nadir angles 20±808 and four azimuth angles (along, against and twice across the plane of the sun rays) is close to the across temperature and it also agrees well with the ®xedsensor temperature measured under 458 to the east, near noon. The roughness length for wind speed zou, has a constant value of 1.75 m independent of wind speed and direction. The roughness length for temperature zot depends on the de®nition of the effective surface temperature. The use of the highest temperature, the along temperature, results in zou ˆ zot. De®ning the effective surface temperature as the mean temperature over all measured directions, represented by the ®xedsensor temperature at noon, gives ln(zou/zot) ˆ ÿ0.5. This value also gives the best ®t between sensible heat ¯uxes calculated from surface temperature and the ones measured by an eddy correlation system. Very thin needles most likely cause a nearzero 'bluff-body contribution to this value. It turns to negative because of the high eddy diffusivity for heat within the roughness sublayer and in the canopy layer. Acknowledgements M. MoÈlder performed this work during a Ph.D. position funded by the Swedish Natural Science Research Council (contract number G-AA/GU 01923). The eddy correlation data were provided by Achim Grelle. This work has been carried out within the framework of NOPEX Ð a northern hemisphere climate processes land-surface experiment. The data used in this investigation are stored in SINOP Ð the system for information in NOPEX.

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