Energy Balance Of A Sparse Coniferous High-Latitude Forest Under Winter Conditions

ENERGY BALANCE OF A SPARSE CONIFEROUS HIGH-LATITUDEFOREST UNDER WINTER CONDITIONS

SVEN-ERIK GRYNING and EKATERINA BATCHVAROVA?

Risø National Laboratory, Roskilde, Denmark

H. A. R. DE BRUINWageningen University, Wageningen, The Netherlands

(Received in final form 31 August 2000)

Abstract. Measurements carried out in Northern Finland on radiation and turbulent fluxes over asparse, sub-arctic boreal forest with snow covered ground were analysed. The measurements repres-ent late winter conditions characterised by low solar elevation angles. During the experiment (12–24March 1997) day and night were about equally long. At low solar elevation angles the forest shadesmost of the snow surface. Therefore an important part of the radiation never reaches the snow surfacebut is absorbed by the forest. The sensible heat flux above the forest was fairly large, reaching morethan 100 W m−2. The measurements of sensible heat flux within and above the forest revealed thatthe sensible heat flux from the snow surface is negligible and the sensible heat flux above the foreststems from warming of the trees. A simple model for the surface energy balance of a sparse forest ispresented. The model treats the diffuse and direct shortwave (solar) radiation separately. It introducesa factor that accounts for the shading of the ground at low solar elevation angles, and a parameterthat deals with the partial transparency of the forest.

Input to the model are the direct and diffuse incoming shortwave radiation. Measurements ofthe global radiation (direct plus diffuse incoming shortwave radiation) above the forest revealed aconsiderable attenuation of the global radiation at low solar elevation. A relation for the atmosphericturbidity as function of the solar elevation angle is suggested. The global radiation was simulated fora three month period. For conditions with a cloud cover of less than 7 oktas good agreement betweenmodel predictions and measurements were found. For cloud cover 7 and 8 oktas a considerable spreadcan be observed. To apply the proposed energy balance model, the global radiation must be separatedinto its diffuse and direct components. We propose a simple empirical relationship between diffuseshortwave and global radiation as function of cloud cover.

Keywords: Boreal forest, Canopy energy balance, Flux profile measurements, Global radiation atlow solar elevation angles, Shading from trees, Winter time.

1. Introduction

The high-latitude boreal forest is inhomogeneous with abundant lakes, mires andconiferous canopies. The boreal forest covers 12× 106 km2 extending as a broadband across the continents of North America, Europe and Asia. It has an import-ant influence on the surface albedo and the local climate (Robinson and Kukla,? Permanent affiliation: National Institute of Meteorology and Hydrology, Bulgarian Academy of

Sciences, Sofia, Bulgaria.

Boundary-Layer Meteorology99: 465–488, 2001.© 2001Kluwer Academic Publishers. Printed in the Netherlands.

466 SVEN-ERIK GRYNING ET AL.

1984; Thomas and Rowntree, 1992). General circulation (or Global climate) mod-els (GCM) suggest that the interactions between snow cover and forest can causelarge changes to the global climate. Bonan et al. (1992) and Thomas and Rowntree(1992) have investigated the sensitivity of GCMs to the specification of the landsurface parameters, and found a marked decrease of temperature associated withthe removal of the forest. This was primarily related to the increase in albedo.The predictions of GCMs with increasing CO2 levels show that the high-latitudein the Northern hemisphere can expect to experience the larger increase in thetemperature (Räisänen, 2000).

The current GCMs have a very simple representation of the interaction betweensnow and forest. Harding and Pomeroy (1996) pointed out that a more completedescription is to be made. The interest in the energy balance of the boreal foresthas resulted in international experiments such as NOPEX (NOrthern hemisphereclimate Processes land-surface EXperiment) (Halldin and Gryning, 1999) with thewinter field campaign WINTEX (WINTer EXperiment) (Harding et al., 2001),BOREAS (Boreal Ecosystem-Atmosphere Study) (Sellers et al., 1997) and theSiberian campaigns described in Hollinger et al. (1998) and Kelliher et al. (1998).

The boreal forest has a low albedo. The snowfall does not stay long on thecanopy, particularly if the solar radiation is large, or the wind is strong. How-ever, even when snow covers the forest canopy, the multiple reflections within thecanopy scatter rather than reflect the incident radiation and the albedo remainslow (Harding and Pomeroy, 1996; Oke, 1987). Betts and Ball (1997) found thatthe forest albedo increases in winter with snow under the canopy. They estimatedrepresentative daily average albedo values for conifer sites of 0.08 in summer and0.13 during the winter. Harding and Pomeroy (1996) report albedo values of 0.16for snow-free and 0.18 for snow covered forest in March. Studies by McFadden andRagotzkie (1967), Federer (1968), Robinson and Kukla (1984, 1985) and Ottermanet al. (1984) state similar low values for the forest albedo in winter. Betts et al.(1998) report that the forest canopies have a lower albedo than other vegetated sites.Lakes also have a low albedo in summer but a high albedo in winter when frozenand snow covered. The use of excessively high albedo values in the NumericalWeather Prediction (NWP) models without accounting for the albedo reductiondue to shading by the trees leads to model surface temperatures as much as 5–15 Klower than the observed (Betts and Ball, 1997; Betts et al., 1996, 1998).

The effect of the shading of the snow covered ground by the forest canopy interms of a view factor has been discussed by Wilson and Petzold (1973), and amathematical model was formulated to calculate the flux of solar radiation to amelting snow surface in sub-arctic woodlands. In commonly used Soil-Vegetation-Atmosphere Transfer (SVAT) models such as SiB (Sellers et al., 1986) and BATS(Wilson et al., 1987) the effects of shading are not discussed, but the partialtransparency of the canopy for solar radiation is taken into account.

In this paper we consider the energy balance and temperature profile for a sparsesub-arctic boreal forest. Turbulence measurements carried out in Northern Finland

ENERGY BALANCE OF A SPARSE CONIFEROUS HIGH-LATITUDE FOREST 467

and Canada reveal that on clear days in March the sensible heat flux can reach morethan 100 W m−2, Batchvarova et al. (2001a), Harding and Pomeroy (1996). Thisvalue seems high for the low solar elevation and the fully snow covered ground,which is a very effective reflector for shortwave radiation. However, at those lowsolar elevation angles most of the snow-covered ground is shaded. We present asimple parameterisation of the surface energy balance of a sparse sub-arctic coni-ferous forest, that is able to account for the effect of a snow covered ground, treesand the shading effect at low solar elevation angles. The parameterisation is basedon partitioning of the global shortwave radiation into diffuse and direct radiationparts, and differs primarily from existing approaches (Deardorff, 1978; Shuttle-worth and Wallace, 1985) in the description of the shortwave radiation balance.In order to facilitate the use of the suggested energy balance parameterisation,expressions for the global (shortwave or solar) radiation and its partitioning into itsdiffuse and direct radiation parts for sub-arctic conditions with low solar elevationangles are suggested. The parameterisation for the shortwave radiation is based onthree months of hourly radiation measurements and cloud cover observations at asite in Northern Finland.

2. Site and Instrumentation

As part of the WINTEX study, meteorological measurements of energy fluxes werecarried out in March 1997 at the Sodankylä Meteorological Observatory (67◦22′ N,26◦38′ E) at Tähtelä in Finnish Lapland. The area is typical for the sub-arctic North-ern Finland with coniferous forests and large open mires dominating the landscape.The river Kitinen flows a few hundred metres west of the Observatory. The townSodankylä is located 6 km north of the Observatory. The area is rather flat both onsmall and large scales, with hills reaching 500 m height within 20 km. During theexperimental period the ground was covered with snow reaching a maximum depthof 100 cm. The river and lakes were frozen and snow covered. The trees most ofthe time were without snow cover. Day and night were approximately equally long.The solar elevation angle was less than 23◦ at noon.

The observatory is located in a dry heath forest of typically 6–8 m tall Scots pine(Pinus sylvestris L.) trees. The distance between the trees is irregular. There aregroups of trees inside which the distance ranges from 1 to 4 m. Irregular distributedtrees in more open areas of different size are also present. The coverage of the treecrowns was roughly estimated to be 50%. The pine trees are relatively young withstem diameter of 5 to 15 cm at breast height.

The instrumentation of the site during the experiment was rather comprehens-ive. Wind and temperature fluctuations were measured with a frequency of 10 Hzby the use of ultrasonic anemometers (Solent Research 3D sonic anemometers) inand above the sparse forest, mounted on a mast at heights of 2, 6, 12 and 18 m. Inaddition measurements of humidity fluctuations were performed at 18 m height by

468 SVEN-ERIK GRYNING ET AL.

use of an OPHIR optical hygrometer. From these measurements half-hourly valuesof wind speed and direction, fluxes of momentum and sensible heat at the fourlevels and the latent heat at the upper level were determined. The measurementprogramme started on March 13 and ended on March 24, 1997.

One of the objectives of the study was to obtain experience in continuous run-ning of sonic anemometers and optical hygrometers under harsh winter conditions.The data showed that the resolution was adequate to extract turbulent fluxes. Theinstruments functioned well, except for a few occasions with rime formation on thesensors, leading to erroneous, but easily recognised values.

As part of the continuous observation programme at the Sodankylä Meteorolo-gical Observatory, hourly averaged measurements of global and diffuse (by use of ashading ring) shortwave radiation were performed. Pyranometers made by Kipp &Zonen model CM11 mounted at 16 m height well above the forest to obtain a freehorizon were used. Hourly observations of cloud cover were performed as part ofthe standard synoptic observation programme. Radiation measurements and cloudcover observations for a 3-month period (March–May 1997) are analysed in thispaper. The relative humidity of the air was measured at 1.5 m height at a clearingin the forest.

3. Fluxes in and above the Forest

3.1. MEASUREMENTS

The temperatures at 2 and 18 m are shown in Figure 1 (left panel), representing theconditions at the forest floor just above the snow pack and above the forest. Theamplitude of the temperature variation at 2 m is seen to be larger than at 18 m. It ischaracteristic that during daytime the temperature decreases with height, which istypical for an unstable atmosphere and associated generally with positive heat flux.During night the temperature increases with height, typical for a stable atmosphere.

Figure 1 (right panel) shows the sensible heat flux at 2 and 18 m heights. Theamplitude of the sensible heat flux is more pronounced for the measurements at18 m compared to the measurements at 2 m. It is seen that during daytime, thesensible heat flux above the forest is noticeably larger than near the forest floor.This indicates that the heat flux is caused by warming of the trees by the incomingradiation. During night-time the sensible heat flux above the forest is smaller thannear the forest floor. The latent heat flux is measured at 18 m height only, and istypically about 10 W m−2 during daytime and becomes smaller during night-time,Figure 4.

It is a very characteristic feature of the measurements that a pronounced gradientin the temperature and sensible heat flux can be observed between the measure-ments near the forest floor and the measurements above the forest, Figure 2. Thefigure shows an example of the temperature and sensible heat flux profiles during

ENERGY BALANCE OF A SPARSE CONIFEROUS HIGH-LATITUDE FOREST 469

Figure 1. Temperature (left panel) and sensible heat flux (right panel) at 2 and 18 m height as afunction of time.

daytime and night-time. In order to illustrate further the behaviour of the dailyvariation of the temperature and sensible heat flux in and above the forest, thediurnal variations of the temperature and heat flux, averaged over the experimentalperiod, were calculated. Figure 3 (upper panel) shows the daily variation of the av-eraged temperature for the period 13 to 23 March, based on half hourly temperaturemeasurements. Near the forest floor the temperature has its minimum approxim-ately an hour past midnight, then it increases slowly reaching a maximum at 1600LST (local standard time), when the temperature starts to fall rapidly. Above theforest (18 m) the minimum temperature during the night is larger and the maximumtemperature during the day is smaller than inside the forest. Thus the temperatureamplitude inside the forest is larger than above the forest. It is also characteristicthat the temperature stratification inside the forest is usually stable and it is neutralor unstable above the forest. The sensible heat flux, plotted in the same way, isshown in Figure 3 (lower panel). It is seen that the heat flux is negative (downwarddirected) during the night. It is also characteristic that the heat flux during daytimeincreases between the forest floor and the top of the forest, reaching a maximumvalue at noon of 100 W m−2 above the forest as compared to only 10 W m−2 nearthe forest floor.

3.2. A SIMPLE MODEL OF THE FLUXES ABOVE THE FOREST

At low solar elevation angles the canopy absorbs an important portion of the dir-ect solar radiation. Since the canopy is sparse it is partly transparent to radiation.However, the ground is covered by snow, which has a very high albedo. Most ofthe solar radiation reaching the snow will be reflected and the canopy will absorb apart of this reflected radiation also. Therefore for direct solar radiation the apparent

470 SVEN-ERIK GRYNING ET AL.

Figure 2. Measured profiles of temperature (left panel) and sensible heat flux (right panel) fornight-time and day-time conditions.

vegetation cover of the forest is greater than the actual one (defined as the portionof the ground covered by vegetation projected vertically).

Here we present a simple parameterisation of the energy balance of thissparse sub-arctic coniferous forest. This parameterisation differs from existingapproaches, primarily in the description of the shortwave radiation balance.

3.2.1. Shortwave RadiationIn the model proposed by Deardorff (1978) the incoming shortwave radiation forthe vegetation (subscriptc) is

Knc = (1− ac)σfK↓ (1)

and for the soil part (subscripts, which is snow in our case),

Kns = (1− as)(1− σf )K↓, (2)

whereKn denotes the net shortwave radiation,K↓ is the incoming shortwave ra-diation across a horizontal plane at the top of forest,a is the albedo andσf thevegetation cover. Note that in Deardorff’s model the vegetation is assumed to beopaque for solar radiation.

It is proposed here to distinguish between direct and diffuse incoming solarradiation

K↓ = D + I sinα, (3)

in whichD is the diffuse component ofK↓ andI the the incoming solar radiationat the top of the vegetation across a plane perpendicular to the solar beam. Since

ENERGY BALANCE OF A SPARSE CONIFEROUS HIGH-LATITUDE FOREST 471

Figure 3.Average temperature (upper panel) and sensible heat flux (lower panel) shown as functionof height and time of the day. The plots are based on half hourly measurements at 2, 6, 12 and 18 mheight for the period 13 to 24 March 1997.

the path through the atmosphere depends on the solar elevation angleα, in generalD andI are expected to be a functionsα.

In order to describe the effect of low solar elevation angles leading to an appar-ently high vegetation cover for direct radiation a shading factorfsh is introduced.If the ground is shaded entirely thenfsh = 1, and when the shading is only directlyunder the trees corresponding to a sun at zenithfsh = σf . For instance iffsh = 0.8,80% of the ground is shaded and 20% receives direct sunshine. The variation of theshading factor is restricted to the rangeσf ≤ fsh ≤ 1. In addition, we introducea transparency factorτ describing the fact that the forest canopy is not opaque for

472 SVEN-ERIK GRYNING ET AL.

shortwave radiation. Ifτ = 1 the canopy is entirely transparent, ifτ = 0 the canopyis opaque.

The critical solar elevation angle,αc below which the ground is fully shaded,corresponding tofsh = 1, can be estimated as (Appendix A):

tanαc = 4h

πd

(σf

1− σf), (4)

whereh andd are typical tree height and crown diameter. When the solar elevationangle is larger thanαc, fsh can be estimated from

fsh = σf(

1+ 4h

πd tanα

)α ≥ αc. (5)

The gain (superscript G) of shortwave radiation for the canopy is:

KGc = σfD + fsh(1− τ)I sinα + σf as(1− τ)KG

s . (6)

The shortwave radiation received by the canopy consists of three terms. The firstrefers to the diffuse solar radiation. The diffuse radiation is treated as in Deardorff(1978), which means the canopy is assumed to be opaque for diffuse radiation andreceivesσf of the total incoming diffuse radiation. The second term refers to thedirect radiation received by the canopy and the third term describes the reflectedshortwave radiation received by the canopy from the snow cover. In the last termKGs is the shortwave radiation received by the snow cover:

KGs = (1− σf )D + fshτI sinα + (1− fsh)I sinα. (7)

Multiple reflected radiation (e.g., from snow to vegetation and next reflected backto snow) is ignored, because the albedo of the vegetation is rather low.

The loss (superscriptL) terms for the canopy and the snow are given by:

KLc = acKG

c (8)

and

KLs = asKG

s (9)

in whichac andas are the albedo for the canopy and the snow respectively. For thenet shortwave radiation of the canopy and the snow we obtain:

Knc = KG

c −KLc (10)

and

Kns = KG

s −KLs . (11)

ENERGY BALANCE OF A SPARSE CONIFEROUS HIGH-LATITUDE FOREST 473

3.2.2. Longwave RadiationFor the parameterisation of the longwave radiation it is assumed that the canopycan be replaced by a flat horizontal plate with emissivity similar to the canopy. Theplate emits radiation towards the atmosphere and towards the snow surface. Theone-sided loss of longwave radiation of the canopy per unit (projected) area of thecanopy, is in this way:

LOc = εcσT 4c , (12)

in which εc is the emissivity of the canopy,σ the Stephan–Boltzmann constantandTc the absolute canopy temperature. The gains of longwave radiation for thecanopy,LGc and the snow surface,LGs are:

LGc = σf εcL↓atm+ σf εcLLs , (13)

LGs = (1− σf )εsL↓atm+ σf εsLOc , (14)

whereL↓atm is the incoming longwave radiation from the atmosphere. The longwave radiation emitted from the canopy and snow surface,LLc andLLs are:

LLc = 2σfLOc , (15)

LLs = εsσT 4s , (16)

whereεs is the emissivity of the snow andTs the absolute temperature of snowsurface. Therefore, the longwave radiation balance for the canopy,Lnc = LGc −LLc ,and snow surface,Lns = LGs − LLs read:

Lnc = σf εcL↓atm+ σf εcεsσT 4s − 2σf εcσT

4c , (17)

Lns = (1− σf )εsL↓atm+ σf εcεsσT 4c − εsσT 4

s . (18)

3.2.3. Energy BalanceThe energy balance for the canopy is simplified. It is assumed that the trees are notable to transpire because the canopy temperature is well below zero. In addition, theheat storage in the vegetation is ignored. This means that the canopy net radiationQnc = Kn

c + Lnc , equals the sensible heat flux:

Qnc = Hc. (19)

The energy balance of the snow surface reads:

Qns = Hs + λEs +Gs, (20)

474 SVEN-ERIK GRYNING ET AL.

in which Qns = Kn

s + Lns is the net radiation for the snow surface,Hs is thesensible heat flux for the snow surface,Es the snow evaporation,λ the latent heatof sublimation andGs the heat flux inside the snow.

Having determined the radiation balance of the forest canopy it is possible toestimate the temperaturesTs, Tc and the fluxes within and above the forest byuse of a simple approach suggested by Deardorff (1978) and Shuttleworth andWallace (1985). The approach is based on a network of resistances. Details and thegoverning equations are given in Appendix B.

3.3. VALIDATION OF THE MODEL

The model was used to simulate the measurements from Sodankylä. The resist-ances suggested by Shuttleworth and Wallace (1985) were applied. As input weused the measurements of wind speed and temperature at 18 m above the forest,the measured global and diffuse radiation above the forest, the humidity of the airat 1.5 meter height measured in a clearing of the forest and observations of thetotal cloud cover. Table I summarises the parameters that were used to describe thesite. Displacement height for the forest, emissivities and albedo of snow and forestare taken after Oke (1987). Price and Petzold (1984) suggest 3–4% lower valuesof the emissivities for the boreal forest during snow melt. However, the modelis not sensitive to such small variations of the emissivities. Based on turbulencemeasurements, Batchvarova et al. (2001b) estimated the forest roughness lengthfor the Sodankylä site to be 1.4 m. Figure 4 (upper panel) shows the modelled andmeasured sensible and latent heat fluxes for the entire measuring period. The scatterplots of the measured and modelled fluxes, Figure 5, show better performance ofthe model for the sensible heat flux compared to the latent heat flux. The agree-ment between measurements and simulations of the sensible heat flux is betterduring daytime than during night time, Figure 4. During night time good agree-ment between model predictions and measurements of the sensible heat flux areobserved for a cloud-covered sky (15/16 March). At reported clear skies, however,the simulated sensible heat flux is two times lower than the measured (16/17 and17/18 March) and near constant. When repeating the simulation assuming a cloudcovered sky, the agreement between model and measurements for the sensible heatflux during the nights of 16/17 and 17/18 March was good. Thus the performance ofthe model during night-time depends on the accuracy of the matching cloud coverobservations, which are known to be uncertain (Figure 4, lower panel). For the lat-ent heat flux a similar difference between day and night in the model performanceis not observed, Figure 4.

In order to show main features of the model, the energy balance terms andtemperatures from the simulation of the conditions on March 15, a sunny cloudlessday followed by a cloudy night, are illustrated in Figure 6. During daytime thecanopy is generally warmer compared to the air inside the canopy,T0, the snowsurface,Ts , and the air above the forest,Tr , giving rise to a flux of heat from the

ENERGY BALANCE OF A SPARSE CONIFEROUS HIGH-LATITUDE FOREST 475

TABLE I

Parameters for the simulation of the Sodankylä experiment.The resistances are parameterised according to Shuttleworthand Wallace (1985). Displacement height, emissivities andalbedo values are according Oke (1987).

Reference height,zr , 18 m

Forest tree height,h, 8 m

Forest displacement height,df dh, 5 m

Forest roughness length,z0, 1.4 m

Forest leaf area index, 2

Forest albedo,ac, 0.1

Forest emissivity,εc, 0.99

Mean boundary layer resistance per unit area,rb, 25 s m−1

Vegetation cover,σf , 0.5

Shading factor,fsh, 1

Transparency factor,τ , 0.5

Snow surface roughness,zs , 0.001 m

Snow surface albedo,as , 0.8

Snow surface emissivity,εs , 0.99

Snow layer conductivity,λs , 0.15 W m−1 K−1

Deep Snow Temperature,Tsd , 270 K

Depth ofTsd , zsd , 0.1 m

Latent heat of sublimation,λ, 2.83× 106 J kg−1

canopy to its surroundings. Because the intermediate level (with temperatureT0)is warmer than the snow, the sensible heat flux for the snow surface is negative,and almost equal but of different direction than the latent heat flux. The heat fluxinside the snow is marginal except in the morning hours, where it contributes tothe warming of the snow surface. It can be noted that the snow surface is warmerthan the air above the forest throughout most the day, except for the late afternoonwhen the radiative cooling makes its temperature to fall below that of the air abovethe forest. During night the air above the forest is warmer than the canopy and thesnow resulting in a downward directed sensible heat flux. The intermediate level iswarmer than the snow and the canopy resulting in sensible heat flux directed to thesnow surface and the canopy.

It is noted that the measured higher temperature in the air during night withinthe canopy compared both to the temperature of the snow and above the forest isnot reproduced by the model, Figures 2 and 3. A possible explanation might be thatthe heat capacity of the canopy is not incorporated in the model (Monteith, 1981;Melas et al., 2001).

476 SVEN-ERIK GRYNING ET AL.

Figure 4.Simulated sensible (full line) and latent heat flux (dashed line) above the forest. Measure-ments at 18 m of sensible and latent heat fluxes are shown as (#) and (4) – upper panel. Observedtotal cloud cover – lower panel.

The sensitivity of the simulated temperatures and fluxes to changes of the forestcoverage are illustrated with Figure 7. A simulation was performed for a case wherethe forest coverage was reduced from 0.5 to 0.2. Thus the site was covered 20per cent by forest and 80 per cent by snow, all other parameters were unchanged.Comparing Figures 6 and 7 it can been seen that the applied reduction of the forestcoverage only changes the total sensible heat flux by about 10 per cent, and thelatent heat flux remains nearly unchanged. However, the temperature of the snowsurface is considerably modified. It is generally lowered by several◦C, and thesnow surface is now colder than the air above the forest throughout the wholeday. The temperature of the forest canopy,Tc andT0, are rather insensitive to thereduced forest coverage.

ENERGY BALANCE OF A SPARSE CONIFEROUS HIGH-LATITUDE FOREST 477

Figure 5.Scatter plots of measured and modelled sensible (left panel) and latent (right panel) heatfluxes above the forest (18 m).

Figure 6.Example of simulated temperatures (left panel) and fluxes (right panel). The conditions on15/16 March 1997 at Sodankylä are simulated. Daytime is cloudless with strong insolation and thenight is cloudy (Figure 4). The fraction of the forest coverage in the simulation is 50%, correspondingto actual conditions.

4. Incoming Solar Radiation

The global radiation at the site during this part of the year is characterised by lowsolar elevation angles.

During the passage through the atmosphere, the shortwave radiation is absorbedby gases, aerosols and dust, which results in a warming of the air. Especially ozoneand water vapour are efficient absorbers of shortwave radiation, but many othergases act as well (Kondratyev, 1969). The amount of absorption depends on thelength of the path through the atmosphere and therefore is a function of the solar

478 SVEN-ERIK GRYNING ET AL.

Figure 7.As in Figure 6 but for a forest coverage of 20%.

elevation angle. At low solar elevation angles the path becomes very long and onlya small part of the shortwave radiation reaches the ground. Pielke (1984) suggeststhat the effect of the solar elevation angle on the absorption is proportional tosin(α)−0.3, and Berlage (1928) that it influences the absorption as an exponentialfunction of sin(α)−1.

Based on 11 years of measurements at the Blue Hill Meteorological Obser-vatory of Harvard University (42◦13′ N, 71◦7′ W), Haurwitz (1945) deduced anempirical relation for the shortwave radiation for a cloud free day:

K↓0 = 1100 sin(α)exp

(−0.059

sin(α)

), (21)

whereK↓0 is the incoming global radiation that reaches the surface. Introducingthe atmospheric turbidity as the fraction of the solar radiation that makes it tothe surface from a cloud free sky,K↓0 /S0 sin(α), whereS0 is the solar constant,Figure 8 shows the turbidity as a function ofα. The crosses show measurementsfor cloud free conditions at the Sodankylä Meteorological Observatory in March,April and May 1997. The relationship suggested by Haurwitz (1945) follows nicelythe overall behaviour of the measurements but is generally too small, especiallyat high solar elevation angles. This likely reflects that the air at the SodankyläMeteorological Observatory is cleaner and therefore a less efficient absorber ofshortwave radiation as compared to the more polluted air at Blue Hill Observatory.The full line in Figure 8 illustrates the relationship

K↓0 = 1250 sin(α)exp

(−0.06

sin(α)

)(22)

that accounts for the cleaner air at Sodankylä by adapting the empirical constantin Equation (21) to the measurements. The number 1250 is in units of (W m−2).

ENERGY BALANCE OF A SPARSE CONIFEROUS HIGH-LATITUDE FOREST 479

Figure 8. Fraction of the shortwave radiation that reaches the ground (atmospheric turbidity) asfunction of the solar elevation angle for cloud-free conditions during the period March 10 to May26, 1997. The new model, Equation (22), and the expression of Haurwitz (1945) are illustrated.Measurements are represented by hourly averages.

Kasten and Czeplak (1980) suggest the following correction to account for theeffect of clouds:

K↓ = K↓0 (1− 0.75C3.4), (23)

whereC is fractional cloud cover (N is the total cloud cover in Oktas:C = N/8).The suggested formula for the global radiation at Northern latitudes is a slightlysimplified combination of Equations (22) and (23):

K↓ = 1250 sin(α)exp

(−0.06

sin(α)

)(1− 0.7C3.4), (24)

whereK↓ is the global solar radiation near the ground, andα is the solar elevationangle.

Figure 9 (upper left panel) shows simulated employing Equation (24), andmeasured incoming solar radiation for all cloud conditions. Overall the agreementis good but with some spread. To investigate the spread in more detail modelledand measured incoming radiation for total cloud cover N≥ 7, N≤ 6 and N≤ 4 areshown in Figure 9. The agreement is indeed good when N≤ 4 and only slightly

480 SVEN-ERIK GRYNING ET AL.

Figure 9.Modelled and measured incoming global radiation. Upper left panel – all cloud conditions,upper right panel – total cloud cover N≥ 7 oktas, lower left panel – total cloud cover N≤ 6 oktasand lower right panel – total cloud cover≤ 4 oktas.

degraded for N≤ 6, whereas the agreement for N≥ 7 is poor. This indicates thatthe major part of the uncertainty is related to total cloud cover 7 or 8. It is evidentthat to lump all cloud types together is a gross oversimplification, and thereforeleads to uncertainty in the modelled cloud cover correction. It is a good result thateven up to cloud cover N = 6 the agreement is fair.

In the foregoing section, it was demonstrated that the direct and diffuse short-wave radiation contribute to the heat balance and the resulting temperatures in asparse forest in very different ways. It is therefore of interest to devise a simplemethod that can be used together with the energy balance parameterisation putforward in the foregoing section, to partition the global radiation into its direct anddiffuse components. Based on the hourly measurements of global and diffuse short-wave radiation, and hourly synoptic observations of cloud cover at the Sodankylä

ENERGY BALANCE OF A SPARSE CONIFEROUS HIGH-LATITUDE FOREST 481

Figure 10.Ratio between diffuse and global radiation as function of total cloud cover. The measure-ments were grouped into classes of the total cloud cover before calculating the averages. The (#)shows averages of the cloud cover groups 0–1, 2–3, 4–5, 6–7 and 8 with the cloud cover in oktas.The measurements are based on the period March 10 to May 26, 1997. The full line indicates theempirical relationship given by Equation (25).

Meteorological Observatory, the ratio between the diffuse and global radiation isplotted as function of the observed total cloud cover, Figure 10. The measurementscover the period March 10 to May 26, 1997. An empirical approximation for theratio of diffuse to global radiation,D/K↓, as function of the total cloud cover isshown in Figure 10:

D/K↓ = 0.2+ 0.2C + 0.5C2. (25)

A natural refinement of Equation (25) would be to establish similar relationshipsfor different types of cloudiness, but to retain simplicity this will not be attemptedhere. In Figure 10 it can be seen that for a cloud-free day the diffuse radiationconstitute about 20 per cent of the global radiation. In a similar way, it can be seenthat for a sky fully covered with clouds the direct radiation is about 10% of theglobal radiation.

482 SVEN-ERIK GRYNING ET AL.

5. Discussion

The measurements presented in this study show that the forest has a pronouncedeffect on the local meteorology. The forest induced sensible heat flux is comparableto those found in central Europe. The trees have low albedo and thus are an efficientabsorber of shortwave radiation. The ground is covered with snow that reflectsshortwave radiation. The upward directed heat flux above the forest originatesmainly from the warming of the trees, while the heat flux from the forest floorremains small. The sensible heat flux can reach more than 100 W m−2 during theday and is able to form a convective mixed layer that can reach depths of typically1000 m in the late afternoon (Batchvarova et al., 2001b). The latent heat flux,which originates mainly from sublimation of snow, is 10 times lower, typically10–20 W m−2.

A model for the energy balance of the forest is presented. Model simulationsshow that for cloud-free conditions with ample global incoming radiation, the heatflux of the forest is to a high degree controlled by the shading effect of the trees,and is not very sensitive to the actual fraction of surface occupied by forest. Thesimulation of the conditions on March 15, 1997 revealed only a slight change inthe sensible heat flux over the forest when the forest coverage was reduced from50 to 20 percent. Under overcast conditions during the day when the main part ofthe incoming radiation is diffuse, similar simulations show, as expected, that thesensible heat flux is sensitive to the forest coverage. The performance of the modelduring night-time depends on the observed cloud cover. The set of parameters,Table I, used in the model reflect late winter and autumn conditions with ratherlong days, a snow covered ground surface and trees. These conditions are typicalfor the Northern boreal forest during the last part of the winter (February to May)and autumn (September and October). However the model is applicable to otherconditions when applying the relevant set of parameters.

Under low solar elevation angles the canopy is apparently fully covering theground, implying that it absorbs an important part of the direct radiation, and onlya minor part reaches the snow surface. Therefore methods based on the distributionand relative coverage of land surface types that do not consider the shading effectof the trees at low solar elevation angles are likely to fail under cloud-free con-ditions. The albedo that can be derived from satellite and airplane measurementsis not the albedo that controls the absorption of shortwave radiation under cloud-free conditions with low solar elevation angles. The effective albedo is not only afunction of the surface coverage but also of the solar elevation angle. For cloudyconditions, the direct radiation is small compared to the diffuse radiation. Theshading effect of the trees is negligible and the use of traditional methods basedon land-use classifications can be better justified.

The shading effect is not only confined to a sparse forest. Similar effects can beexpected in high-latitude urban environments, where the sensible heat flux abovethe urban area will be controlled by the thermal characteristics of the urban canopy

ENERGY BALANCE OF A SPARSE CONIFEROUS HIGH-LATITUDE FOREST 483

and to a lesser degree by the thermal characteristics of the surface. However thegeometry of the urban structure is very different from a forest, so modified schemesmight be needed.

A new expression for the incoming shortwave radiation has been suggested,that is adapted to high-latitude conditions and low solar elevation angles. Theexpression behaves quite differently at low solar elevation angles as compared tofrequently used models for global radiation (Gryning and Batchvarova, 2001).

In the developed model for the heat flux over the forest, the incoming direct anddiffuse shortwave radiation is shown to control the heat flux in very different ways.To be able to partition the global radiation into its diffuse and direct components, asimple empirical expression of the ratio between the diffuse and global radiation asfunction of cloud cover is suggested. The model is based on the total cloud coverand does not distinguish between the various types of clouds, aerosol content of theatmosphere and other parameters known to influence the global radiation and itspartitioning in diffuse and direct shortwave radiation. It is meant as a simple toolto be used with standard meteorological observations.

The foregoing discussion has been focused on the heat flux at one point ina sparse forest. The area around the measuring point contains also mires andlakes, which have very different thermal and radiation characteristics comparedto the forest. Based on measurements on the evolution of the mixed layer deducedfrom radiosoundings, it is possible to estimate the area averaged sensible heat flux(Gryning and Batchvarova, 1999). The analysis (Batchvarova et al., 2001b) showsthat the modelled area-averaged heat flux is 30 to 50% of the heat flux measuredover the forest.

Acknowledgements

We are grateful to Martti Heikinheimo (the Finnish Meteorological Institute), Ri-gel Kivi (the Sodankylä Meteorological Observatory) for providing the radiationan synoptic data, and to Per-Erik Johansson (the Swedish National Defense Re-search Establishment) for flux data. The hospitality and help of the staff at theSodankylä Meteorological Observatory and the assistance of John Hansen and LarsChristensen are acknowledged. The European Union supported the study, contractnumber ENV4-CT96-0324.

Appendix A. Simple Expression for the Shading Factor

The shading factor,fsh, represents the part of the ground that is covered by treesor lies in the shade of trees. Here we derive a simplified expression for the shad-ing factor, and the critical solar elevation angle, below which the ground is fully

484 SVEN-ERIK GRYNING ET AL.

shaded. Considering a tree with heighth and typical crown diameterd, it covers anarea of:

π

4d2 (A1)

and casts it shade over an area of:

hd

tanα, (A2)

whereα is the solar elevation angle. The total area of ground per tree is:

πd2

4σf. (A3)

At the critical solar elevation angle,αc, the ground is entirely in the shade of thetrees:

π

4d2+ hd

tanαc= πd2

4σf, (A4)

which in Equation (4) has been solved forαc. This condition corresponds tofsh =1 andα ≤ αc.

When the elevation of the sun is higher thanαc, only a fractionfsh of the groundis shaded:

π

4d2+ hd

tanα= πd2

4σffsh, (A5)

which can be solved to yield the expression forfsh given in Equation (5). FromEquations (4) and (5) it can be seen that the variation of the shading factor fallswithin the rangeσf ≤ fsh ≤ 1.

Appendix B. Governing Equations

The fluxes are determined by the resistance method presented by Deardorff (1978)and Shuttleworth and Wallace (1985). The method includes a canopy layer, whichinteracts both with the atmosphere and the underlying surface, Figure B1. Accord-ing to this scheme there is a sensible heat flux, which ‘flows’ through resistanceracfrom the canopy to an artificial level with air temperatureT0. In the same way thesensible heat flux from the snow surface to this level experiences resistanceras andthere is resistanceraa from the intermediate level to the reference level above theforest with temperatureTr . The net radiation for the snow,Qn

s , and for the canopy,Qnc , reads:

ENERGY BALANCE OF A SPARSE CONIFEROUS HIGH-LATITUDE FOREST 485

Figure B1.Illustration of the resistance method.

Qns = Kn

s + εs(1− σf )L↓atm+ εsσf εcσT 4c − εsσT 4

s (B1)

and

Qnc = Kn

c + εcσfL↓atm+ σf εcεsσT 4s − 2σf εcσT

4c . (B2)

These equations can be linearized by using the approximation

T 4s,c ≈ T 4

r + 4T 3r (Ts,c − Tr) (B3)

in whichTs,c is eitherTs or Tc. Then Equations (B1) and (B2) can be approximatedby:

Q∗s = Q∗sr + fs1(Tc − Tr)+ fs2(Ts − Tr), (B4)

Q∗c = Q∗cr + fc1(Tc − Tr)+ fc2(Ts − Tr), (B5)

in whichQ∗sr andQ∗cr are the net radiation of the snow and the canopy respectivelywhen settingTs andTc equal toTr in Equations (B1) and (B2), andQ∗s andQ∗c arethe linearised functions of the net radiation for snow and canopy. In addition theparametersfs1, fs2, fc1 andfc2 are given by

fs1 = 4σf εsεcσT3r , (B6)

486 SVEN-ERIK GRYNING ET AL.

fs2 = −4εsσT3r , (B7)

fc1 = −8σf εcσT3r , (B8)

fc2 = 4σf εsεcσT3r . (B9)

The energy balance equation for snow reads:

Q∗s =ρcp

ras(Ts − T0)+ λEs +Gs (B10)

and that for the canopy:

Q∗c =ρcp

rac(Tc − T0). (B11)

In addition we must have thatρcp

raa(T0− Tr) = ρcp

rac(Tc − T0)+ ρcp

ras(Ts − T0). (B12)

The resistancesraa, ras and rac can be determined from the parameterisationssuggested by Deardorff (1978) or Shuttleworth and Wallace (1985). The heat fluxinside the snow layer,Gs can be evaluated with

Gs = λs (Tsd − Ts)zsd

, (B13)

in which λs is the heat conductivity of the snow, andTsd the snow temperature ata depthzsd. The calculations are simplified ifTsd can be considered constant. Aninspection of the snow temperatures measured at a site near Sodankylä reveals thatduring the course of a day, the temperature at a depth of 10 cm was almost constant.The evaporation (sublimation) from the snow,λEs , can be parameterises followingDeardorff (1978) as

λEs = λρcur(qs − qr), (B14)

whereur is the wind speed at the reference height,c is a parameterisation constanttaken here as 0.001,qs the specific humidity for saturated air at snow surface tem-perature (Ts), andqr the specific humidity of the air at the reference height. Theincoming longwave radiation from the atmosphere, including the effect of clouds,can be expressed as suggested by Paltridge and Platt (1976) and Swinbank (1963):

L↓atm= 5.31× 10−13T 6

r + 60C, (B15)

whereN is fractional cloud cover. Then the temperaturesTs, Tc andT0, and thefluxesQ∗c andQ∗s can be determined by numerically solving the coupled Equa-tions (B4), (B5), (B10), (B11) and (B12). Knowing the temperatures, the modelledsensible and latent heat fluxes can be determined.

ENERGY BALANCE OF A SPARSE CONIFEROUS HIGH-LATITUDE FOREST 487

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