integrating fluxes from heterogeneous vegetation

7
© 2001 Blackwell Science Ltd. http://www.blackwell-science.com/geb 595 ETEMA SPECIAL ISSUE Global Ecology & Biogeography (2001) 10 , 595–601 Blackwell Science, Ltd Integrating fluxes from heterogeneous vegetation F. IAN WOODWARD and MARK R. LOMAS Department of Animal and Plant Sciences, University of Sheffield, Sheffield, S10 2TN, U.K. E-mail: f.i.woodward@sheffield.ac.uk ABSTRACT The vegetated landscape of Europe has been strongly impacted by human management to pro- duce a heterogeneous patchwork of semi-natural and agricultural vegetation varying over a wide range of spatial scales. A model is described for averaging vegetation fluxes from a landscape of forest and grassland into the planetary boundary layer (PBL). At a scale of 1 km, model simulations indicate that vegetation heterogeneity exerts little effect on the PBL and regional fluxes will be simple areal averages of the different vegetation types. Above 5 km the model simulates significant effects of different vegetation types on the whole PBL. Averaging fluxes to the regional scale will there- fore need to consider explicitly the nature, extent and behaviour of different vegetation types. Key words Convection, ecosystem, Europe, for- est, grassland, planetary boundary layer, surface layer, temperature, transpiration, vegetation. INTRODUCTION The European Terrestrial Ecosystem Modelling Activity (ETEMA) is concerned with predicting the functional and structural dynamics of ecosys- tems. In the European landscape, in particular, different vegetation types are heterogeneously distributed over a wide range of spatial scales. The aim of this paper is to define a model for averaging the fluxes of heat, momentum and mass from different vegetation types into the planetary boundary layer (PBL), at spatial scales greater than one km. The typical spatial extents of European vegeta- tion types (from 1 to > 10 km) cover the qual- itative scales of both disorganized and organized heterogeneity (Shuttleworth, 1988; André et al. , 1990). The characteristic length of the organized horizontal scale is > 10 km. At this scale, vegeta- tion heterogeneity can exert effects to the top of the PBL (typically reaching a maximum altitude of 1–2 km). In addition, landscape heterogeneities can also exert meso-scale circulations within the PBL. A typical example would be on- and off-shore breezes. Vegetation heterogeneities such as between irrigated and unirrigated areas (Mahrt et al. , 1994) and at the edges of forests (Bourgealt et al. , 1991) have also been shown to develop meso-scale cir- culation patterns. A disorganized heterogeneity has a horizontal scale of less than about 10 km and exerts min- imal effects on the PBL. In such situations it appears that fluxes from different ecosystems may be averaged by areal extent to provide an effective prediction of the average effect. This approach is known as the tile method (Avissar & Pielke, 1989). The effectiveness of the averaging increases with horizontal wind speed (Avissar & Schmidt, 1998) and recent simulations indicate that the tile method works effectively for predict- ing average fluxes, when the scale of the hetero- geneity is less than about 5–10 km (Avissar & Schmidt, 1998). However, the approach fails to capture flux variations associated with advection across boundaries between different vegetation types. Harding et al . (1997) demonstrate that evapora- tion can be enhanced when moving across the boundary from a dry surface to a wet surface, but evaporation is not equally depressed in the reverse direction. This effect is caused by different humidity gradients close to the boundaries and between the two directions. Similar inequalities, through advective effects, are seen at the bound- ary between rough and smooth canopies. Therefore,

Upload: f-ian-woodward

Post on 06-Jul-2016

217 views

Category:

Documents


0 download

TRANSCRIPT

Page 1: Integrating fluxes from heterogeneous vegetation

© 2001 Blackwell Science Ltd. http://www.blackwell-science.com/geb

595

ETEMA SPECIAL ISSUE

Global Ecology & Biogeography

(2001)

10

, 595–601

Blackwell Science, Ltd

Integrating fluxes from heterogeneous vegetation

F. IAN WOODWARD and MARK R. LOMAS

Department of Animal and Plant Sciences,

University of Sheffield, Sheffield, S10 2TN, U.K. E-mail: [email protected]

ABSTRACT

The vegetated landscape of Europe has beenstrongly impacted by human management to pro-duce a heterogeneous patchwork of semi-naturaland agricultural vegetation varying over a widerange of spatial scales. A model is described foraveraging vegetation fluxes from a landscape offorest and grassland into the planetary boundarylayer (PBL). At a scale of 1 km, model simulationsindicate that vegetation heterogeneity exerts little

effect on the PBL and regional fluxes will be simpleareal averages of the different vegetation types.Above 5 km the model simulates significant effectsof different vegetation types on the whole PBL.Averaging fluxes to the regional scale will there-fore need to consider explicitly the nature, extentand behaviour of different vegetation types.

Key words

Convection, ecosystem, Europe, for-est, grassland, planetary boundary layer, surfacelayer, temperature, transpiration, vegetation.

INTRODUCTION

The European Terrestrial Ecosystem ModellingActivity (ETEMA) is concerned with predictingthe functional and structural dynamics of ecosys-tems. In the European landscape, in particular,different vegetation types are heterogeneouslydistributed over a wide range of spatial scales.The aim of this paper is to define a model foraveraging the fluxes of heat, momentum andmass from different vegetation types into theplanetary boundary layer (PBL), at spatial scalesgreater than one km.

The typical spatial extents of European vegeta-tion types (from

1 to > 10 km) cover the qual-itative scales of both disorganized and organizedheterogeneity (Shuttleworth, 1988; André

et al.

,1990). The characteristic length of the organizedhorizontal scale is > 10 km. At this scale, vegeta-tion heterogeneity can exert effects to the top ofthe PBL (typically reaching a maximum altitudeof 1–2 km). In addition, landscape heterogeneitiescan also exert meso-scale circulations within thePBL. A typical example would be on- and off-shorebreezes. Vegetation heterogeneities such as betweenirrigated and unirrigated areas (Mahrt

et al.

, 1994)and at the edges of forests (Bourgealt

et al.

, 1991)

have also been shown to develop meso-scale cir-culation patterns.

A disorganized heterogeneity has a horizontalscale of less than about 10 km and exerts min-imal effects on the PBL. In such situations itappears that fluxes from different ecosystemsmay be averaged by areal extent to provide aneffective prediction of the average effect. Thisapproach is known as the tile method (Avissar &Pielke, 1989). The effectiveness of the averagingincreases with horizontal wind speed (Avissar &Schmidt, 1998) and recent simulations indicatethat the tile method works effectively for predict-ing average fluxes, when the scale of the hetero-geneity is less than about 5–10 km (Avissar &Schmidt, 1998). However, the approach fails tocapture flux variations associated with advectionacross boundaries between different vegetation types.Harding

et al

. (1997) demonstrate that evapora-tion can be enhanced when moving across theboundary from a dry surface to a wet surface,but evaporation is not equally depressed in thereverse direction. This effect is caused by differenthumidity gradients close to the boundaries andbetween the two directions. Similar inequalities,through advective effects, are seen at the bound-ary between rough and smooth canopies. Therefore,

GEB240.fm Page 595 Monday, October 15, 2001 8:16 PM

Page 2: Integrating fluxes from heterogeneous vegetation

596

F. I. Woodward and M. R. Lomas

© 2001 Blackwell Science Ltd,

Global Ecology & Biogeography

,

10

, 595–601

landscapes with large numbers of edges of thesetypes will have greater rates of evaporation andmomentum transfer than expected from a uniformcanopy of vegetation.

MODEL REQUIREMENTS

A model of the PBL is required for the ETEMAproject that will integrate the fluxes from hetero-geneous vegetation during the daylight developmentof a turbulent PBL. In completing this integra-tion, the PBL will also provide new temperature,humidity and wind speed profiles above the hetero-geneous landscape, which will in turn feed backon the fluxes from the different vegetation types.The aim of the model is to integrate a heightgrowth model of the PBL (e.g. McNaughton& Spriggs, 1986) with a model that integratesthe impacts of heterogeneous landscapes on thesurface layer fluxes (e.g. Klaassen, 1992). Thisapproach therefore aims to account for the changesin fluxes at boundaries between vegetation typesand to integrate these effects to provide an aver-age of the flux driving gradients within the over-lying PBL.

DISORGANIZED HETEROGENEITY

Basic model description

When the heterogeneous landscape has a horizontalscale of less than 10 km then it is assumed thatthe PBL is little influenced by vegetation hetero-geneity of fluxes (Avissar & Schmidt, 1998), althoughits height may change in response to the large-scaleaverage ecosystem fluxes (Brakke

et al.

, 1978).The critical gradients for modifying ecosystemfluxes are in the bottom 100 m surface layer ofthe PBL, where the gradients are strongest andwhere measured fluxes above the vegetation sur-face are very close to the actual surface fluxes.This is the layer in which standard micrometeoro-logical measurements are made.

Fluxes within the surface layer above a hetero-geneous landscape have been determined bymodifications to the model developed initially byLi

et al

. (1985) and subsequently by Klaassen(1992) and Luppes (1993). Horizontal atmo-spheric flow is defined over the landscape and isinfluenced by the variable structures of theunderlying vegetation types. The fluxes from the

vegetation are dependent on wind velocity, tem-perature and humidity and these variables areinfluenced by the fluxes from the different vegeta-tion types. It is necessary, therefore, to determinethe horizontal gradients of these variables and theseare determined from the laws of conservation, asfollows:

(1)

(2)

(3)

(4)

where

u

is the horizontal and

w

the vertical windvelocity,

x

is horizontal and

z

vertical distance,

p

is atmospheric pressure,

s

the air density,

c

p

thespecific heat of air,

q

the specific humidity,

θ

thepotential temperature and

t

the momentum flux.

F

d

and

F

cg

are the ecosystem drag force and coun-ter gradient forces on the horizontal flow.

H

and

E

are the ecosystem fluxes of sensible and latentheat and the subscript

s

indicates source terms.Changes in the horizontal gradients of temper-ature, wind speed and humidity therefore feedback to each canopy layer, directly influencingthe calculated sensible and latent heat fluxesand also, indirectly, by effects of changes inwind speed on the boundary layer resistance andchanges in vapour pressure deficit on stomatalresistance.

The fluxes of momentum, sensible and latent heatare determined from these gradients, as follows:

(5)

(6)

(7)

where

e

and

e

H

are the eddy viscosities formomentum and heat and are determined as:

(8)

(9)

u ∂u∂x------ w∂u

∂z------ 1

σ---∂ p

∂z------+ + 1

σ---∂τ

∂z------ Fd– Fcg+=

∂u∂x------ ∂w

∂z-------+ 0=

u ∂θ∂x------ w∂θ

∂z------+ 1

σcp

-------- ∂H∂z--------– Hs+

=

u ∂q∂x------ w∂q

∂z------+ 1

σ--- ∂E

∂z-------– Es+

=

τ σε ∂u∂z------=

H σcpεH∂θ∂z------–=

E σεH∂q∂z------–=

ε lΦm

-------

2 ∂u∂z------=

εH εΦm

Φh

-------=

GEB240.fm Page 596 Monday, October 15, 2001 8:16 PM

Page 3: Integrating fluxes from heterogeneous vegetation

Fluxes from landscapes

597

© 2001 Blackwell Science Ltd,

Global Ecology & Biogeography

,

10

, 595–601

and where

F

m

and

F

h

are the atmospheric stabilityfunctions for momentum and heat (Webb, 1970;Delage & Girard, 1992) and

l

is the mixing length(Klaassen, 1992).

The vegetation canopy is treated as multilayered,and leaves of leaf area density,

A

l

, within eachcanopy layer, act together to define the drag force

F

d

, which retards the horizontal flow and derivesthe counter gradient force,

F

cg

:

F

d

=

0.08

A

l

u

2

(10)

(11)

(12)

A

lr

is a reference leaf area density,

h

max

the heightof the maximum value of

A

l

and

h

c

is the canopyheight.

The available net radiation,

A

e

, for drivinglatent and sensible heat transfer at any level ofthe vegetation canopy, is defined as:

Ae(z) = Rn(z + ∆z)e−KrAl ∆z − Rn(z − ∆z) (13)

where Rn(z + ∆z) is the net radiant balance of thelayer above the current layer, Kr is the extinctioncoefficient for net radiation in the canopy, ∆z isthe thickness of the leaf layer and Rn(z − ∆z) isthe net radiant balance of the layer below. Theenergy balance of the ground surface is defined as:

Ae = (1 − g)Rn (14)

where g is the ground heat constant, which canvary with soil type.

The latent heat flux in each canopy layer has,in these simulations, been calculated by thePenman–Monteith equation (Monteith, 1965) andthe sensible heat transfer determined as the dif-ference between Ae and the latent heat flux.

(15)

The stomatal, rs, and boundary layer, ra, resist-ance terms for the Penman–Monteith equation

are provided by the underlying ecosystem model.s is the slope of relationship between vapourpressure and temperature, e*a is the saturatedvapour pressure, ea is the vapour pressure at theair temperature of the leaf layer and ν is the psy-chrometric constant. The nature of the vegetationmodels, which model fluxes, is not the criticalcomponent of this modelling exercise, and so anymodels that simulate exchanges of fluxes byvegetation can be incorporated within this modelof PBL transfer.

A series of numerical methods have then beendeveloped, based on earlier ideas of Luppes (1993)to solve the range of simultaneous and differentialequations in the full model.

Model performance

The simulated response of a change in windspeed passing from a heath to a forest and backto a heath (Fig. 1) indicates the marked retardingeffect of the forest on the wind speed, bothwithin the forest but also upwind of the forestand shortly after emerging from the forest. Asimple test of the model has been achieved bycomparison with data measured by Gash (1986)and also used by Klaassen (1992). Gash measuredchanges in wind speed above a heathland after atransition from forest. The wind velocity abovethe heathland increases steadily for at least 1 kmafter the transition, in a manner which is closelysimulated by the model (Fig. 2).

Fcg0.04

1 0.8Alr+---------------------- u hc( ) u–( ) z

hc

----=

Alrmax Al( ) z hmax≤

Al z hmax>

=

λEsAe σcp

e*a ea–ra

-------------- +

s vra rs+

ra

------------- +

-------------------------------------------=

Fig. 1 Modelled changes in wind speed, at a heightof 1.5 m above the ground and across a landscape ofgrassland (300 m) of height 0.2 m, forest (300 m) ofheight 12 m and grassland (300 m).

GEB240.fm Page 597 Monday, October 15, 2001 8:16 PM

Page 4: Integrating fluxes from heterogeneous vegetation

598 F. I. Woodward and M. R. Lomas

© 2001 Blackwell Science Ltd, Global Ecology & Biogeography, 10, 595–601

ORGANIZED HETEROGENEITY

Model description

Organized heterogeneity, on a scale of 10 km orgreater, exerts an effect to the top of the PBL,which may typically be one or two km (Raupach,1991). At these scales the PBL averages outsmaller-scale heterogeneity and provides estim-ates of regional fluxes from the underlyinglandscape. The surface layer, which is modelledwhen investigating disorganized heterogeneity, isabout 10% of the depth of the PBL (Denmeadet al., 1996). The full model therefore aims tosimulate the daytime growth of the whole PBL,which therefore provides the capacity to predictregional-scale fluxes from both heterogeneousand homogeneous vegetation.

The PBL is modelled as a uniform slab be-tween the top of the previously described surfacelayer and the top of the PBL (McNaughton &Spriggs, 1986). This approach recognizes that thePBL is a well-mixed layer so that, unlike thesurface layer, concentrations change little withinthe mixed layer (Denmead et al., 1996). There-fore, the depth of the mixed layer and the meanconcentration of the appropriate scalar deter-mine average or regional fluxes from the land-scape. The PBL is capped by an inversion layer.The height of the PBL grows throughout the daydue to the combined increase in convective flow,originating from the surface layer and by solarheating and entrainment of the usually drier airabove the PBL capping inversion. The PBL depthceases to grow as irradiance falls in the after-

noon. At night the PBL collapses and is replacedby a shallow nocturnal boundary layer, whichis not modelled, and it is assumed that themajor fluxes are defined within the surface layermodule. The rate of change in height of the PBL,dh/dt is defined according to the model of Tennekes(1973):

(16)

where H and λE are provided from the surfacelayer module. The vertical gradient of potentialvirtual temperature above the PBL (available frommeteorological measurements or other model simula-tions), , is defined:

(17)

and where the potential virtual temperature θv

is defined in terms of temperature, T, and specifichumidity, q, as:

θv = (T + Γz)(1 + 0.61q) (18)

where Γ is the adiabatic lapse rate.The change in the concentration of a particu-

lar scalar sm, with time is defined by the surfaceflux density of the scalar, Fs, and the effectsof entrainment and vertical motion in the PBL(Denmead et al., 1996):

(19)

where s+ is the concentration of the scalar justabove the PBL and W+ the vertical wind velocityat the top of the PBL. These latter two variablesmust be provided by another model or data set,although Denmead et al. (1996) discuss methodswhich may circumvent the lack of such data.

Model performance

The simulated daytime evolution of the PBL heightabove a forest and a grassland (Fig. 3) is verysimilar to previous simulations and observations(Lloyd et al., 1996), with slow increases in earlymorning and late afternoon. The PBL is greaterabove the forest because, in this simulation, theresistance to latent heat transfer is greater for theforest and so the sensible heat flux (equation 16)is greater than over the grassland.

Fig. 2 Predicted (—) and observed (j, Gash, 1986)trends in normalized wind speeds for 750 m overheathland, following a transition from forest.

dhdt------ H 0.07λE+

σcphϒθv

-----------------------------=

ϒθv

ϒθv

dθv

dz-------=

dsm

dt--------

Fs

h-----

s+ sm+h

--------------- dh

dt------ W+–

+=

GEB240.fm Page 598 Monday, October 15, 2001 8:16 PM

Page 5: Integrating fluxes from heterogeneous vegetation

Fluxes from landscapes 599

© 2001 Blackwell Science Ltd, Global Ecology & Biogeography, 10, 595–601

The changes in specific humidity with time andheight (Fig. 4) follow the same trends for forestand grassland and feed back on the surface layer,as changes in the flux gradients. The steepestgradients are in the surface layer, which itself canchange in depth, increasing to 200 m by 16.00 h,when the PBL is at its highest in this simulation.The remainder of the PBL is well mixed to theboundary with the inversion cap, and as a con-sequence the specific humidity is constant, inkeeping with theoretical and observational expecta-

tions (Garratt, 1992). In these simulations, theair above the PBL is drier than within the PBL,leading to a sharp transition at the top of PBL.

The combined averaging of fluxes from aheterogeneous landscape within the surface layerand the full PBL has been the overall aim of thismodel development. This averaging is shown fortwo cases of forest followed by grassland, with asimulation of the profile after 1 km of grassland(Fig. 5) and after 5 km of grassland (Fig. 6), dur-ing the middle of the day. The data are presented

Fig. 3 Modelled daytime height growth (m) of theplanetary boundary layer (PBL) over a forest andover a grassland. Canopy height of the forest is 11 mwith a canopy stomatal resistance of 100 s m−1, andthe grassland is 1 m high with a canopy stomatalresistance of 50 s m−1.

Fig. 4 Modelled profiles of specific humidity (g kg–1)above a forest at 2 h intervals. The specific humiditygradient above the PBL is −0.005 g kg−1 m–1 and thetop of the PBL is indicated by the rapid drop inspecific humidity towards the top of each profile.

Fig. 5 Modelled profiles of specific humidity abovea grassland, 1 km after (at time 12.33 pm) a transition(at time 12.00 pm) from a forest (—); profile for acontinuous forest (---).

Fig. 6 Modelled profiles of specific humidity abovea grassland, 5 km after (at time 2.47 pm) a transition(at time 12.00 pm) from a forest (—); profile for acontinuous forest (---).

GEB240.fm Page 599 Monday, October 15, 2001 8:16 PM

Page 6: Integrating fluxes from heterogeneous vegetation

600 F. I. Woodward and M. R. Lomas

© 2001 Blackwell Science Ltd, Global Ecology & Biogeography, 10, 595–601

as though a one-dimensional column of air moves,at the horizontal wind speed, over the land sur-face. In keeping with theory (Avissar & Schmidt,1998), travel over 1 km of grassland has little effecton the whole profile (Fig. 5). After 5 km thereare effects on the whole profile which becomesslightly more humid, with a reduced PBL height(Fig. 6).

CONCLUSIONS

A combined surface-layer and PBL averaging rou-tine has been completed for integrating daytimefluxes over heterogeneous landscapes, such asfound throughout Europe. Both averaging routineswork in accordance with theory and observationand are readily applicable to a wide range offluxes, including CO2 and water vapour. A typicalapplication of the model will be to determineregional fluxes from a heterogeneous landscape ofvegetation, in order to determine impacts on, forexample, stream flow and regional climate (Pielkeet al., 1998; Stohlgren et al., 1998). Such a simula-tion could couple with different vegetation orecosystem models that are capable of simulatingfluxes of energy, mass and momentum. This coup-ling would then also automatically account forthe feed back of the PBL climate on vegetationprocesses. In principle, this model could alsobe used to couple vegetation processes withGeneral Circulation Models, to enhance thetreatment of meso-scale feed backs of vegetationon climate.

ACKNOWLEDGMENTS

This study was funded by the European Union(ETEMA project, ENV4-CT95–0052).

REFERENCES

André, J.C., Bougeault, P. & Goutorbe, J.P. (1990)Regional estimates of heat and evaporation fluxesover nonhomogeneous terrain: examples from theHAPEX-MOBILHY programme. Boundary-LayerMeteorology, 50, 77–108.

Avissar, R. & Pielke, R.A. (1989) A parameterisationof heterogeneous land surfaces for atmosphericmodels and its impact on regional meteorology.Monthly Weather Review, 117, 2113–2136.

Avissar, R. & Schmidt, T. (1998) An evaluation ofthe scale at which ground-surface heat flux patchi-

ness affects the convective boundary layer usinglarge-eddy simulations. Journal of AtmosphericScience, 55, 2666–2689.

Bourgealt, P., Bret, B., Lacarrere, P. & Noilhan, J.(1991) An experiment with an advanced surfaceparameterisation in a mesobeta-scale model. Part II:the 16 June 1986 simulation. Monthly WeatherReview, 119, 2374–2392.

Brakke, T.W., Verma, S.B. & Rosenberg, N.J. (1978)Local and regional components of sensible heatadvection. Journal of Applied Meteorology, 17,955–963.

Delage, Y. & Girard, C. (1992) Stability functionscorrect at the free convection limit and consistentfor both the surface and Ekman layers. Boundary-Layer Meteorology, 58, 19–31.

Denmead, O.T., Raupach, M.R., Dunin, F.X.,Cleugh, H.A. & Leuning, R. (1996) Boundary layerbudgets for regional estimates of scalar fluxes.Global Change Biology, 2, 255–264.

Garratt, J.R. (1992) The Atmospheric Boundary Layer.Cambridge University Press, Cambridge.

Gash, J.H.C. (1986) Observations of turbulence down-wind of a forest–heath interface. Boundary-LayerMeteorology, 36, 227–237.

Harding, R.J., Blyth, E.M. & Taylor, C.M. (1997)Issues in the aggregation of surface fluxes froma heterogeneous landscape: from sparse canopiesup to the GCM grid scale. Scaling-up from cell tolandscape (ed. by P.R. Van Gardingen, G.M. Foodyand P.J. Curran), Society for Experimental Bio-logy Seminar Series 63, pp. 229–251. CambridgeUniversity Press, Cambridge.

Klaassen, W. (1992) Average fluxes from heterogeneousvegetated regions. Boundary-Layer Meteorology, 58,329–354.

Li, Z., Miller, D.R. & Lin, J.D. (1985) A first order clos-ure scheme to describe countergradient momentumtransport in plant canopies. Boundary-Layer Meteoro-logy, 33, 77–83.

Lloyd, J., Kruijt, B., Hollinger, D.Y., Grace, J.,Francey, R.J., Chin Wong, S., Kelliher, F.M.,Miranda, A.C., Farquahr, G.D., Gash, J.H.C.,Vygodskaya, N.N., Wright, I.R., Miranda, H.S. &Schulze, E.D. (1996) Vegetation effects on theisotopic composition of atmospheric CO2 at localand regional scales: theoretical aspects and acomparison between rain forest in Amazonia anda boreal forest in Siberia. Australian Journal ofPlant Physiology, 23, 371–399.

Luppes, R. (1993) Atmospheric flow in heterogene-ous vegetated regions. MSc Thesis, University ofGroningen, The Netherlands.

Mahrt, L., MacPherson, J.I. & Desjardins, R. (1994)Observations of fluxes over heterogeneous surfaces.Boundary-Layer Meteorology, 67, 345–367.

McNaughton, K.G. & Spriggs, T.W. (1986) A mixedlayer model for regional evaporation. Boundary-Layer Meteorology, 34, 243–262.

GEB240.fm Page 600 Monday, October 15, 2001 8:16 PM

Page 7: Integrating fluxes from heterogeneous vegetation

Fluxes from landscapes 601

© 2001 Blackwell Science Ltd, Global Ecology & Biogeography, 10, 595–601

Monteith, J.L. (1965) Evaporation and environment.The state and movement of water in living organ-isms (ed. by G.E. Fogg), Society for ExperimentalBiology Symposium 19, pp. 205–234. CambridgeUniversity Press, Cambridge.

Pielke, R.A., Avissar, R., Raupach, M., Dolman, A.J.,Zeng, X. & Denning, A.S. (1998) Interactionsbetween the atmosphere and terrestrial ecosystems:influence on weather and climate. Global ChangeBiology, 4, 461–475.

Raupach, M.R. (1991) Vegetation atmosphere inter-action in homogeneous and heterogeneous ter-rain: some implications of mixed-layer dynamics.Vegetatio, 91, 105–120.

Shuttleworth, W.J. (1988) Macrohydrology — thenew challenge for process hydrology. Journal ofHydrology, 100, 31–56.

Stohlgren, T.J., Chase, T.N., Pielke, R.A., Kittel, T.G.F.& Baron, J.S. (1998) Evidence that local land usepractices influence regional climate, vegetation, andstream flow patterns in adjacent natural areas. GlobalChange Biology, 4, 495–504.

Tennekes, H. (1973) A model for the dynamics ofthe inversion above a convective boundary layer.Journal of the Atmospheric Sciences, 30, 558–567.

Webb, E.K. (1970) Profile relationships: the log-linearrange and extension to strong stability. QuarterlyJournal of the Royal Meteorological Society, 96, 67–90.

GEB240.fm Page 601 Monday, October 15, 2001 8:16 PM