Evaluation of the energy fluxes including advection: an observation
in a larch forest of eastern Siberia
Hiroki TANAKA**Graduate School of Agriculture, Kyoto Univ., Kyoto 606-8602, JAPANIntroduction
The surface energy flux is one of the important boundary conditions for the dynamics in theatmospheric boundary layer. Recently, the surface heat flux has been observed on various land
surfaces using the eddy covariance method. It has been often reported that the heat flux obtained by
the eddy covariance method (the eddy flux) is less than the available energy for the heattransportation and only 60-90% of the available energy (e.g. Fitzjarrald and Moore, 1994; Moore etal., 1996; Shuttlewordth et al., 1988; Thompson, 1979; Lee and Black, 1993; Ohta et al., 2001).
Most observations for the eddy flux consider the heat transportation caused by around 100~103 mscale of eddy. The eddy fluxes do not include the advection flux caused by relatively larger eddy orother mechanisms. In this study, the total heat fluxes including the eddy and the advection fluxes areevaluated using the observation results in a larch forest of eastern Siberia.

Site and materials
Observation was carried out on a micrometeorological observation tower installed at around 20 km
north of Yakutsk, Russia (62.08oN, 129.75oE). The site is located on the permafrost region and a flatlarch forest with decline of 1.6 o toward to the northeast. The latitude is 220 m (a.s.l.). The depth of
the active layer is 1.2 m. The mean height of larch trees which constitute the forest canopy is around18 m. The stand density is 840 trees par hectare. The leaf area index obtained by a plant canopyanalyzer (LI-COR, LI-2000) is 1.2 during summer. There is an understorey of berry species with
0.05 m height.
The observation of the eddy heat fluxes over the canopy was carried out from 14th June throughrd23 July in 1998. The fluxes were computed using the data obtained by an ultra sonicanemo-thermometer (KAIJO, DA-600) and an infrared gas analyzer (LI-COR, LI-6262) installed at
32 m high. The other meteorological factors including the wind velocity, short and long wave
radiations, air temperature, and the atmospheric humidity are observed over and below the canopy
simultaneously.

Basic equations
The energy balance equation above forest is described as follow,S solar − S ref . + Latm. − Lsurface = H + λE + G + P(1)

here, Ssolar is the solar radiation, Sref is the reflective short wave radiation from canopy, Latm is thedownward long wave radiation, Lsurface is the upward long wave radiation, H is the sensible heat flux,
λE is the latent heat flux, G is the change in the heat storage in the forest including the undergroundlayer, and P is the energy for the photosynthetic activities of forest canopy. The equation 1 issimplified as follow,
R NET − G = H + λE
(2)here, RNET is the net radiation, and P is ignored as negligibly small. The left term is the available
energy for heat transport, and the right term is the total heat flux. The heat fluxes are divided into
two components including the eddy flux (eddy) and the advection flux (adv). Finally, the energybalance equation is described as follow,
R NET − G = H eddy + H adv. + λEeddy + λE adv.
(3)
The eddy fluxes are obtained by the observation using the eddy covariance method, while theadvection fluxes are represented as the product of the difference between temperature (T, oC) orvapor density (q, g m-3) of the outgoing (out) and incoming (in) air, and the volume (V, m3 m-2 s-1) ofmixing air, as follows;H adv = ρC P (Tout − Tin ) × V(4)

λE adv = λ (q out − qin ) × V(5)

here, ρ is the atmospheric density (g m ), CP is the specific heat at constant pressure (=1.01, J g-1 ℃-1), and λ is the latent heat (J g-1). The volume of mixing air is computed according to the equation 3,4, and 5 simultaneously as follow,-3

V =R NET − G − H eddy − λE eddy

ρC P (Tout − Tin ) + λ (qout − qin )(6)

here, V ≥ 0 .

Application for the actual condition
In this site, the air at the trunk space is warmer and more humid than the air above canopy in thedaytime. In case that the both air is mixed, warm and humid air goes out from forest and cool anddry air comes into forest. As the result, the sensible and latent heat advection fluxes are upward.
Similarly in the nighttime, the sensible heat advection flux is downward and the latent heat advection
flux is upward, since the air at the trunk space is cooler and more humid. This mechanism might
explain the heat transportation between the forest and the atmosphere caused by relatively larger
eddy or other mechanisms. In this study, therefore, the temperature and vapor density observed at31.4 m high and 5.7 m high are adopted as the representative temperature and vapor density of theoutgoing and incoming air.
The hourly sensible heat advection flux is computed as around 40 % of the total sensible heatflux. The daily mean sensible heat advection flux is only 10 % of the total sensible heat flux becauseof the counteracting between the effect at night and in the daytime. On the other hand, the dailylatent heat advection flux is computed as more than 30 % of the total latent heat flux. Especially inthe morning, the latent heat advection flux is larger than the eddy flux. The diurnal course of thetotal latent heat flux seems to have good agreement with physiological analysis for plants.

Summary
The sum of eddy fluxes obtained by the observation of the fluxes at a larch forest in eastern Siberia
is only 80% of available energy. The analysis using canopy conductance model suggests that thelatent heat flux is possible to be underestimated. On the other hand, the analysis using co-spectra
model suggests that the effect of the eddy in low frequency band can be underestimated. Theadvection flux is defined as the transportation caused by larger scale mixing of atmosphere. The
advection heat fluxes are computed as the product of the heat difference of the mixing air and themixing volume. It is assumed for the actual condition that the incoming air is the atmosphere above
forest canopy, and that the outgoing air is the atmosphere at trunk space. The total heat fluxes
including the eddy and advection flux are around 10% larger than the eddy flux for sensible heat,
and around 50% larger than the eddy flux for latent heat.

References
Fitzjarrald, D.R., and Moore, K.E. (1994) Growing season boundary layer climate and surface
exchanges in a subarctic lichen woodland. J. Geophys. Res. 99, 1899-1917
Lee, X., and Black, T.A. (1993) Atmospheric turbulence within and above a Douglas-fir stand. PartII. Eddy fluxes of sensible heat and water vapor Bound.-Layer Meteorol. 64, 369-389
Moore, K.E., Fitzjarrald, D.R., Sakai, R.K., Goulden, M.L., Munger, J.W., and Wofsy, S.C. (1996)
Seasonal variation in radiative and turbulent exchange at a deciduous forest in Central
Massachusetts. J. Appl. Meteorol. 35, 122-134
Ohta, T., Hiyama, T., Tanaka, H., Kuwada, T., Maximov, T.C., Ohata, T., and Fukushima, Y. (2001)
Seasonal variation in the energy and water exchanges above and below a larch forest in eastern
Siberia. Hydrol. Process. 15, 1459-1476
Shuttleworth, W.J., Gash, J.H.C., Lloyd, C.R., McNeill, D.D., Moore, C.J., and Wallace, J.S., (1988)
An integrated micrometeorological system for evaporation measurement. Agric. For. Meteorol.
43, 295-317
Thompson, N. (1979) Turbulent measurements above a pine forest. Bound.-Layer Meteorol. 16,293-310