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A water balance model to study the hydrological response to

A water balance model to study the hydrological response to
A water balance model to study the hydrological response to

A water balance model to study the

hydrological response to different scenarios of deforestation in Amazonia

Cassiano D’Almeida a,*,Charles J.Vo

¨ro ¨smarty a,b ,Jose ′A.Marengo c ,George C.Hurtt a ,https://www.sodocs.net/doc/3d12224940.html,wrence Dingman b ,Barry D.Keim d

a

Complex Systems Research Center,University of New Hampshire,Morse Hall,Durham,NH 03824,USA b

Department of Earth Sciences,University of New Hamsphire,James Hall,Durham,NH 03824,USA c

Centro de Previsa

?o do Tempo e Estudos Clima ′ticos,Instituto Nacional de Pesquisas Espaciais,Cachoeira Paulista,SP 12630-000,Brazil d

Department of Geography and Anthopology,Louisiana State University,Baton Rouge,LA 70803,USA

Received 6September 2005;received in revised form 2May 2006;accepted 9May 2006

Summary Amazonia encloses some of the largest watersheds in the world,experiencing sub-stantial amounts of rainfall annually and producing more runoff to the ocean than any other region.Amazonia experiences one of the highest rates of deforestation in the world and the hydrological effects of such a disturbance have already been investigated by several studies.Contrasting results exist,especially when different scales and degrees of heterogeneity are considered.This paper assesses the dependency of the hydrological impact of deforestation on these factors through application of a gridded water balance model.The model simulates different scenarios of deforestation based on straightforward water balance calculations.In all experiments performed,the scenarios conform to observations of decreased evapotranspi-ration within disturbed sites.Initially,by implying an uncoupling between small deforested a ′reas and circulation,the model suggests an increase in runoff locally.However,when the land-atmosphere coupling caused by intermediate levels of deforestation is reproduced through deviations on circulation,the model con?rms that the water cycle may or may not become regionally accelerated,depending on the degree of heterogeneity associated.Finally,by sim-ulating a scenario of complete deforestation,the model con?rms expectations of a less intense water cycle in Amazonia.Due to the broad range of numerical models and observation networks currently available,the importance of the proper representation of both scale and heterogene-ity of deforestation to the correct assessment of its hydrological effects is emphasized.

KEYWORDS

Deforestation;Amazonia;

Water balance model;Spatial scale;Heterogeneity

0022-1694/$-see front matter

c 2006Elsevier B.V.All rights reserved.doi:10.1016/j.jhydrol.2006.05.027

*Corresponding author.Tel.:+551231868572.E-mail address:cassiano@cnpq.br (C.D’Almeida).

Journal of Hydrology (2006)331,125–

136

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journal homepag e:www.elsevi e r.c o m /l o c a te /j h y d r o l

Despite our model results,there is need for more mechanistic studies on coupled land-sur-face and atmosphere interactions under varying conditions.

c2006Elsevier B.V.All rights reserved.

Introduction

The Amazon River represents the largest watershed in the world,with a drainage area of$7million km2(Sioli, 1984a).Including adjacent watersheds to the east(like Tocantins Basin),the region holds more than40%of all remaining tropical rainforests in the world(Laurance et al.,2001).Such an extensive vegetation cover maintains high levels of evapotranspiration(Franken and Leopoldo, 1984;Vo¨ro¨smarty et al.,1989;Salati and Nobre,1991;Vic-toria et al.,1991),which in turn,sustains a great portion of the local rainfall following the recycling of precipitation (Brubacker et al.,1993;Eltahir and Bras,1994;Trenberth, 1999;Bosilovich and Chern,2006).Through atmospheric teleconnections,the Amazonian rainforest is also critical to both regional and global climates(Eagleson,1978;Zeng et al.,1996;Marengo and Nobre,2001;Werth and Avissar, 2002).Currently,the region faces one of the highest defor-estation rates in the world(Fig.1;INPE,2004),following what has been taking place in the tropics for some time, where the rainforest is being replaced by soy bean planta-tion and pastures.The impact of land-cover changes on cli-mate and water cycle dynamics have been investigated (Charney et al.,1975;Eagleson,1982;Williams and Balling, 1996)and documented regionally in various parts of the globe(Calder et al.,1995;Hetzel and Gerold,1998;van Langenhove et al.,1998;Cherkauer et al.,2000;Yin and Li,2001;Goteti and Lettenmaier,2001;Yang et al.,2002).Particularly in Amazonia,the impact of deforestation on climate has been extensively studied over the last few decades.This impact has been evaluated under many differ-ent conditions,especially at different scales and under dif-ferent scenarios of deforestation.

Overall,results to date indicate that in all spatial scales, deforestation in Amazonia imposes a decrease in evapo-transpiration(Sioli,1984b;Shuttleworth,1988;Nepstad et al.,1994;Rocha et al.,1996,2004).At the local scale, deforestation also causes an increase in runoff(Gentry and Lopez-Parodi,1980;Williams and Melack,1997;Costa et al.,2003),which on the contrary,is generally expected to decrease following a complete deforestation scenario (Lean and Warrilow,1989;Lean and Rowntree,1993;Pol-cher and Laval,1994;Sud et al.,1996;Costa and Foley, 2000).Regarding the imposed effect on precipitation,it is also likely to decrease after extreme scenarios of deforesta-tion(Nobre et al.,1991;Henderson-Sellers et al.,1993;Manzi and Planton,1996;Lean et al.,1996;Lean and Rowntree, 1997;Hahmann and Dickinson,1997;Voldoire and Royer, 2004),although local disturbances do not seem to be large enough to signi?cantly affect its regime.Additionally,it has been noted that regional areas of clearing may or may not be able to increase cloud formation and potentially rain-fall(Pielke et al.,1991;Chen and Avissar,1994;Avissar and Liu,1996;Avissar and Schmidt,1998;Baidya Roy et al., 2003),depending on the degree of heterogeneity imposed on the land-cover.Therefore,apparently con?icting

results Figure1Spots(black dots)with the highest rates of deforestation in Brazil’s Legal Amazonia(main?gure)(INPE,2004),as observed by LANDSAT images(small squares).Geographic location(left?gure)of Legal Amazonia and of the area considered in our study with in South America,including Amazon and Tocantins Basins plus nearby watersheds to the northeast(thick lines).

126 C.D’Almeida et al.

exist.However,despite all the uncertainties involved,such contrasts are not necessarily or exclusively associated with the consistency of the numerical models employed,or with the accuracy of the observations performed.Rather,they seem to be related to intrinsic and interrelated scale and heterogeneity dependencies on the hydrological effects of deforestation.This paper investigates such dependencies in detail through application of a water balance model(see ‘‘A water balance model of deforestation’’).The application of a set of different scenarios of deforestation into the mod-el enables assessment of the importance of the size of the clearing area(see‘‘Effects of scale’’),as well as of its spa-tial con?guration(see‘‘Effects of heterogeneity’’),to the overall hydrological impact of deforestation in Amazonia.

A water balance model of deforestation

To assess the impact of deforestation at different scales and under different degrees of spatial heterogeneity,a model based on conservation of mass principles and on a scheme linking land-surface to atmosphere within a gridded domain was developed.The model is intended to represent consis-tency and tendency with respect to the hydrological impact of deforestation–and speci?cally to this effect alone.The analysis focus on steady-state solutions of the model,even though it has not been designed for quantitative applica-tions such as climate predictions.Its assumptions and parameterizations are kept straightforward,but in keeping with results from the literature(Nobre et al.,1991;Eltahir and Bras,1994;Williams and Melack,1997;Costa et al., 2003;Marengo,2004).

The model was designed to relate the main?uxes(precipi-tation(p),evapotranspiration(e),runoff(r),water vapor con-vergence(c),in mm yrà1)and stocks(atmosphere(w a),soil (w s),in mm)of water within a generic gridded domain.The model is based upon the following mass–balance equations:

d w a=d t?eetTàpetTtcetTe1Td w s=d t?petTàeetTàretTe2T

which are solved simultaneously for the water stock terms on each gridcell in the domain.The water?ux terms are cal-culated as linear functions of the water stock values:petT?k1w aetTe3TeetT?k2w setTe4TretT?k3w setTe5TEstimated values of w a and w s in Amazonia were used as the initial conditions for both stocks of water(Jipp et al.,1998; Kuznetsova,1990),while annual water budget estimates of p,e,r and c for this region(Roads,2002)were used to initialize the water?uxes.The constant factors k1,k2and k3were then set after the application of these amounts into Eqs.(3)–(5) (Table1).Therefore,these factors tend to stabilize the sys-tem throughout the experiments,making it converge to its long-term mean at steady-state–or,to a state only slightly away from such mean conditions in the disturbed scenarios.

All model integrations were initialized with a one-year spin-up period.During this period,no deforestation is em-ployed by the model and the system converges to its primary steady-state.Following initialization,deforestation is then induced through the application of a factor(d)determining the fractional disturbance over the entire domain for each scenario as:absent(d=0),complete(d=1)or partial (0

F?Ne1àdTe6TD?Nde7T

After application of the disturbance,the system moves to-ward a different state of equilibrium for each scenario.Ini-tially,the only perturbation imposed on deforested gridcells is a reduction in the corresponding evapotranspiration?ux (e d)–in agreement with various observations in Amazonia (Hodnett et al.,1995;Jipp et al.,1998):

e d?k4ee8Twhere k4(0

f gridcells.

Table1Variables and parameters used by our water balance model

Symbol Variables and parameters Initial value Unit Reference

w a Water in the atmosphere40.mm Kuznetsova(1990)

w s Water in the soil440.mm Jipp et al.(1998)

p a Precipitation1930.mm yrà1Roads(2002)

r a Runoff760.mm yrà1Roads(2002)

e a Evapotranspiration1430.mm yrà1Roads(2002)

c a Water vapor convergence630.mm yrà1Roads(2002)

k1Precipitation factor48.2yrà1–

k2Evapotranspiration factor28.8yrà1–

k3Runoff factor12.7yrà1–

k4Evapotranspiration factor0.1––

n Number of bordering gridcells–––

k5Attenuation factor0.46yrà1–

a When displayed with the subscript f,it refers to mean?ux over forested gridcells,and with the subscript d,it refers to mean?ux over deforested gridcells;with no subscripts,it refers to the mean?ux over the entire domain.

A water balance model to study the hydrological response to different scenarios of deforestation127

Several parameters involved with the dynamics of defor-estation,e.g.albedo,in?ltration and interception,were not explicitly considered by the model.It was assumed that the hydrological impact of deforestation induced by these parameters were implicitly and qualitatively incorporated through the changes imposed in evapotranspiration–since the energy available for the latent heat?ux in the surface goes down as albedo goes up with deforestation–and through the local increase in runoff obtained by the model (see‘‘Model experiments’’)–in accordance to the impact of decreased in?ltration and interception that occurs along with deforestation.

Model experiments

Modeling experiments were performed to test the hydrolog-ical impact of deforestation under different scenarios of deforestation within an idealized gridded domain.To be comparable in size to Amazonia($7million km2),the do-main was set to have N=280,000(25km2in area)gridcells. The scenarios employed differed in two respects:the extent (or,domain fraction)of deforestation,and the degree of heterogeneity.Model results were evaluated and compared in terms of mean changes to:precipitation,evapotranspira-tion and runoff,over both disturbed and undisturbed grid-cells,and also averaged over the entire domain.

Effects of scale

The hydrological response to deforestation is controlled by several factors,which are not simultaneously dominant at particular spatial scales.Different extents of deforestation are therefore,expected to induce distinct,possibly con-trasting effects.While local disturbances are expected to affect the water cycle exclusively within the disturbed area –by decreasing evapotranspiration and increasing runoff–scenarios of regional and complete deforestation are ex-pected to generate a wider impact,potentially signi?cant even on climate.Due to its size,Amazonia is likely to even-tually exhibit all of these responses at different stages of deforestation.In our model,the direct comparison between water?ux changes predicted for individual disturbed and undisturbed gridcells offers an estimation of direct,local-ized impacts of deforestation,while changes averaged across the entire domain reveals its aggregated,regional-ized impact.Furthermore,each particular scenario repre-senting a different extent of deforestation leads to a particular state of equilibrium,thus enabling the evaluation of the scale dependency in the response to each scenario considered.At this point,scenarios with the same extent of deforestation were all linked to the same degree of heterogeneity.

Constant precipitation(constant P)

The?rst analysis performed with the model was aimed on reproducing the effects of deforestation when a noticeable effect on circulation is not enabled,resembling the impact of local areas(<102km2)of clearing.To do so,both precip-itation and water vapor convergence terms were assumed constant throughout the integrations.Despite being repre-sentative of only the initial stages of deforestation,these conditions were repeatedly applied to all levels of clearing in the domain.Naturally,negative anomalies of mean

do-Figure2Changes on mean(a)domain?uxes,(b)evapotranspiration,and(c)runoff for scenarios with different fractions of deforestation,calculated as the difference(in mm yrà1)between steady-state values for each scenarios and the corresponding value for the control simulation.Changes on(a)mean domain?uxes of evapotranspiration and runoff were respectively marked with squares and balloons,while corresponding changes in precipitation refer to the unmarked line.Mean changes on(b and c)forested and deforested gridcells were respectively marked with triangles and circles,while the mean domain changes refer to the unmarked lines. 128 C.D’Almeida et al.

main evapotranspiration,in comparison to the control sim-ulation(Fig.2a),were suggested by the model(following Eq.(8)).The opposite occurred to the mean domain runoff, in agreement with?ndings from one of the few,if not the only,observational study that compiled runoff measures in a small catchment in Amazonia,both before and after clear-ing(Williams and Melack,1997).Regarding the mean grid-cell values of both evapotranspiration and runoff,they varied by the same amount for all levels of deforestation (Figs.2b and c,respectively)and therefore,changes in mean domain values were only due to the number of for-ested and deforested gridcells at each scenario.It then fol-lows that by assuming an absolute uncoupling between local land-surface disturbances and precipitation,the changes in mean domain?uxes of evapotranspiration and runoff are expected to be linearly and spatially aggregated as the ex-tent of deforestation increases.

Uniform precipitation(uniform P)

A scenario allowing deforestation to slightly and progres-sively in?uence the local pattern of precipitation was also simulated by the model,aiming to take into account the importance of the recycling of moisture in Amazonia(Bru-backer et al.,1993;Eltahir and Bras,1994;Trenberth, 1999).Precipitation was allowed to vary according to the mean basin stock of water in the atmosphere(Eq.(3)),thus still being spatially uniform throughout the entire domain–following the assumption of a‘‘well-mixed’’atmosphere. As a result of the overall decline in the atmospheric stock of water following the decrease in evapotranspiration on deforested gridcells,the mean domain precipitation at equilibrium decreased as the level of deforestation in-creased(Fig.2d).At the same time,the mean basin evapo-transpiration stabilized at lower values in comparison to the previous experiment as deforestation progressed,also showing a higher decrease over deforested gridcells (Fig.4e).Regarding runoff,the model predicted opposite changes over different gridcell types.It showed enhanced runoff over deforested gridcells and diminished runoff over forested gridcells,even though both values decreased as deforestation progressed,while the mean basin runoff sta-bilized at its initial value for all levels of deforestation (Fig.2f).According to Eqs.(1)and(2),such invariance in the mean basin runoff follows directly from the imposed invariance in the mean basin water vapor convergence, since it equals the equilibrium value that runoff must converge to at steady-state.The invariance in runoff also explains why both mean basin precipitation and evapotrans-piration decreased at the same proportional rate as defores-tation,while the simultaneous occurrence of such reductions indicate that the precipitation recycling contrib-utes to the weakening of the water cycle as the impact of local disturbances gets linearly accumulated.

Variable water vapor convergence(variable C) Compared to the scenarios above,regional areas of defores-tation(102–105km2)are expected to induce a stronger, potentially signi?cant land–atmosphere interaction(Silva-Dias and Regnier,1996;Dolman et al.,1999;Wang et al., 2000;Baidya Roy and Avissar,2002).To reproduce the ef-fects of such interactions,our model aimed on incorporat-ing anomalies on circulation induced by the spatial heterogeneities associated to fragmented areas of clearing. To do so,the water vapor convergence?eld was then forced to change.These changes were included in the model by increasing the water vapor convergence term(c d)over deforested gridcells and decreasing its analogous term(c f) over forested gridcells.The deviation in the mean conver-gence?eld over a gridded domain was then derived based on the scheme represented by Fig.3,which illustrates the expected in?uence of the boundaries between forested(in gray)and deforested(in white)gridcells on circulation. The arrows correspond to the enhanced horizontal diffusion of water vapor into deforested areas–as a result of the gra-dients of temperature and pressure generated–and there-fore,they are inversely dependent on the number of arrows departing from the same source cell.For simplicity,the ar-rows departing from each?rst-order gridcell(labeled with 1)are assumed to be twice as intense as the arrows depart-ing from each second-order gridcell(labeled with2),three times as intense as the arrows departing from each third-order gridcell(labeled with3),and so on.It then gives that each one of the n gridcells located along the borders be-tween forested and deforested areas contribute equally to the change imposed in circulation.Additionally,the conver-gence change over forested and deforested gridcells is as-sumed to be directly proportional to the water vapor stock(w af)over the source(forested)gridcells,giving that: c f?càk5nw af=Fe9Tc d?ctk5nw af=De10TThe k5factor[Tà1]is an adjusted parameter(k5=0.46)that delays the imposed effect on circulation in such a way that evapotranspiration over deforested gridcells never gets increased as a result of deforestation,in keeping with

Eq. Figure3Scheme representing the impact of different spatial distributions of forested(in gray)and deforested(in white) gridcells on circulation,as simulated by our model for variable C and decaying C experiments.The arrows represent the anomalous horizontal diffusions of water vapor imposed for(a) 0.04,(b)0.20,(c)0.36and(d)0.96fractions of deforestation, while the numbers refer to the quantity of arrows departing from each forested(source)gridcell.

A water balance model to study the hydrological response to different scenarios of deforestation129

(8).The response to the changes imposed in water vapor convergence(Eqs.(9)and(10))as simulated by our model in this scenario were then summarized as follows.

Similarly to both previous analyses,evapotranspiration decreased for all levels of deforestation(Fig.4b).At the same time,runoff was predicted to increase on deforested gridcells and decrease on the forested ones,while its mean domain value still did not display any changes,regardless of the deforestation level applied(Fig.4c).Compared to re-sults above,the greatest change was noted in the impact on precipitation,which showed a slight increase over defor-ested gridcells at low levels of deforestation,while both forested and mean basin values decreased for all levels (Fig.4a).Despite the general tendency for deforestation to ultimately weaken all water?uxes in Amazonia,the re-sults presented here agree with indications that the land-atmosphere coupling induced by regional,fragmented areas of clearing may induce a noticeable ampli?cation of the cy-cle.Furthermore,since such ampli?cation is restricted to moderate levels of clearing,the predictions at high levels are in reasonable agreement with the impact of deforesta-tion expected at the large scale.

Decaying water vapor convergence(decaying C)

In this experiment,along with the?uctuations expressed above,the convergence term was progressively and linearly reduced as a function of the size of the clearing,in agree-ment with?ndings of some modeling studies that predict a decrease in mean water vapor convergence under scenar-ios of extensive deforestation(Shukla et al.,1990;Dickinson and Kennedy,1992;Polcher and Laval,1994b;McGuf?e et al.,1995).The tendency for a decay in the mean domain water vapor convergence term could be associated not only to the local impact of land-surface disturbances,but also to low-frequency oscillations in the atmosphere induced by re-mote forcings(Chu et al.,1994;Marengo,2004,2005).Our model suggests both decreasing precipitation(Fig.4d)and evapotranspiration(Fig.4e)as a response to a complete scenario of deforestation,while following moderate scenar-ios of deforestation it suggests an increase in precipitation. Due to the decreasing pattern on water vapor convergence, this time the mean basin runoff also decreased,forcing the mean runoff over deforested gridcells to decrease as well, as deforestation moved to levels nearing completion (Fig.4f),in agreement with previous modeling results(No-bre et al.,1991;Lean et al.,1996;Costa and Foley, 2000).In addition,the decrease in convergence caused a further decrease in both evapotranspiration and precipita-tion in comparison to results above.

Effects of heterogeneity

Land-surface heterogeneity–or,simply fragmentation–is an intuitive concept that can be understood in several dif-ferent ways according to the context in which it is consid-ered.Due to its close association with the impoverishment of forest ecosystems(Bierregaard et al.,2001)and with the increase in?re vulnerability around areas of clearing (Alvarado et al.,2003),land-surface heterogeneity has been typically de?ned and evaluated under an ecological frame-work.The quanti?cation method proposed by Rudel and Ro-per(1997),for example,suggests that fragmentation in any disturbed domain should be calculated as the ratio of the forest–nonforest boundary extent and the intact area,link-ing patchiness and clumpiness with high and low levels of heterogeneity,respectively.Therefore,according to this and other similar methods(Olff and Ritchie,2000;Ritters et al.,2000),an almost entirely disturbed domain

contain-Figure4Same as in Fig.2,but for variable C and decaying C experiments.Mean changes(a–c)on forested and deforested gridcells were marked with triangles and circles,while the mean domain changes refer to the unmarked lines.

130 C.D’Almeida et al.

ing only a small and localized forested area is regarded as highly fragmented.This outcome clearly indicates an eco-logically oriented approach,since it de?nes heterogeneity according to the disturbance upon the remaining forested area only,neglecting its impact on the surrounding areas al-ready disturbed.However,since the evaluation of the over-all hydrological impact of deforestation on any disturbed domain would necessarily include its entire area,the impor-tance of heterogeneity in such a context would not be ade-quately accounted for by this method.Hence,a similar method that estimates the degree of heterogeneity over any disturbed domain as the ratio of forest-nonforest boundary extent (or perimeter;pr )to the total area of the domain (A )is de?ned here,as spatial heterogeneity (h ):h ?pr =A

e11T

As suggested earlier,land-surface heterogeneities are expected to in?uence the local climate in Amazonia,espe-cially when associated with regional scenarios of deforesta-tion.Since any particular extent of deforestation may be linked to several different geospatial patterns,not all such scenarios of deforestation are necessarily able to induce a signi?cant effect in the atmosphere.In order to show that,our model was then aimed at comparing the hydrological ef-fects of not only different extents of deforestation,but also of different spatial distributions of the disturbance.

Clearly,the perimeter of deforestation (which is equiva-lent to n ,in Eqs.(9)and (10))depends not only on the extent of deforestation,but also on the degree of heterogeneity associated with each scenario.Therefore,to test for the in?u-ence of deforestation scenarios with different degrees of het-erogeneity on circulation,our model evaluated the response to different relations between n and d (see ‘‘Varying spatial heterogeneity (varying H )’’).In the experiments above,a somewhat regular expansion of deforestation linking the dif-ferent fractions of deforestation considered was used (Fig.5).Such a relation shows that intermediate levels of deforesta-tion generates the longest border between the two distinct areas and therefore,tends to induce a greater effect on circu-lation.Similarly,it shows that for low and extreme levels of clearing,the perimeter of deforestation approaches zero,and so does the spatial heterogeneity associated.

Varying spatial heterogeneity (varying H )

The method of quanti?cation proposed above was then ap-plied to a wide range of scenarios of deforestation (Fig.6)sorted according to the fraction of area disturbed (columns)and to an ‘‘intuitive’’degree of heterogeneity (rows).Such an ‘‘intuitive’’degree of heterogeneity can be understood as the smallest fractional (or,individual)disturbance present on each row of scenarios.The spatial heterogeneity index (h )associated with each one of these scenarios –calculated by Eq.(11)–appears in Fig.7a,while each curve in the graphic refers to a particular row of scenarios in Fig.6.In every row,the highest spatial heterogeneity value occurs at moderate levels of deforestation,while all scenarios approaching both absent and total clearing (where pr =0)are linked to its low-est values.Scenarios on Fig.6differ among each other only in terms of n ,which is exactly the quantity that reproduces the effect of land-surface heterogeneity on circulation as im-posed by our water balance model.The n ·d pro?les associ-ated with the curves in Fig.6are depicted in Fig.7b,which shows the manner in which the scenarios with contrasting levels of spatial heterogeneity affect the water vapor con-vergence ?eld.The top curves in Figs.7a and b indicate that the scenarios with the maximum spatial heterogeneity at each level of deforestation are responsible for the greatest impact on circulation.This reveals the importance of the spatial resolution employed (by gridded models,or observa-tions)to the potential impact of spatial heterogeneity on cir-culation.The gridcell area is equivalent to the smallest possible fractional area considered,thus making the magni-tude of such an impact inversely proportional to the spatial resolution of the grid.Our model was then used to simulate the hydrological effects of all the scenarios in Fig.6and to evaluate the impact of their contrasting degrees of spatial heterogeneity on these effects.

According to results from previous studies (Wang et al.,2000;Baidya Roy and Avissar,2002;Baidya Roy et al.,2003),the most relevant impact of land-surface heterogene-ities on climate tend to occur on precipitation,which may or may not increase over disturbed areas due to the anomalous convection induced.The mean changes of precipitation over the deforested gridcells (p d )linked to the scenarios in Fig.6are shown in Fig.8a,which con?rms that the increase in the local rainfall caused by land-surface heterogeneities are most likely observed over moderate levels of deforestation –for instance,at d =0.16.However,it also shows that even at this particular level of clearing,the impact of fragmenta-tion may not be strong enough to compensate for the predic-tion of a general weakening of the water cycle.The average changes to precipitation over the forested area (p f )are pre-dicted to decrease for all degrees of spatial heterogeneity (Fig.8b),while the precipitation averaged over the entire domain decays linearly for all cases and at the same exact rate (Fig.8c).This last result is directly linked to the assumption that with no ?uctuations on the mean basin water vapor convergence,signi?cant changes induced at the regional scale may not be detected at the basin scale.Furthermore,it indicates that independent –and poten-tially remotely induced (Chen et al.,2001;Fu et al.,2001;Foley et al.,2002;Marengo,2004,2005)–?uctuations on the water vapor convergence ?eld would make it even harder to detect such

changes.

Figure 5Relation of the number of bordering gridcells [n ]to the fraction of deforestation as determined by Eq.(11),which speci?es the impact of land-surface gradients on the horizontal water vapor diffusion (as exempli?ed in Fig.2).

A water balance model to study the hydrological response to different scenarios of deforestation 131

Discussion

The hydrological effects of deforestation in Amazonia are subject to intrinsic and interrelated scale and heterogeneity dependencies.This implies that the size and fragmentation

of the disturbed areas may determine whether the water cy-cle in the basin becomes intensi?ed or weakened under par-ticular deforestation scenarios.In this perspective,apparently con?icting results at different scales,or under different degrees of heterogeneity,are in fact part of

the

Figure 6Scenarios of deforestation with different distributions of forested (in gray)and deforested (in white)gridcells,as simulated by the model in varying H experiment.Scenarios within each column experience the same extent of deforestation,while the scenarios within each row have the same fractional area of

clearing.

Figure 7Number of bordering gridcells [n ](a)and spatial heterogeneity [h ](b)linked to the scenarios in Fig.6.Points marked with squares,circles,triangles,and ·-crosses refer to scenarios with minimum,low,high and maximum degrees of heterogeneity,respectively.

132 C.D’Almeida et al.

same complex system in witch different factors prevail at different conditions.At local scales,the prevailing factor is the uncoupling between land-surface disturbances and circulation,which leads to an increase in runoff along with a decrease in evapotranspiration,without signi?cant changes in precipitation.At regional scales,depending on the degree of heterogeneity associated,the land–atmo-sphere coupling induced by fragmentation may or may not become a factor,potentially inducing an increase in cloud formation and rainfall.Following a complete deforestation in Amazonia,the weakening on the recycling of moisture is expected to be the dominant factor,ultimately contribut-ing to diminish all water ?uxes in the region.Such scenarios of deforestation were simulated in the present work by a water balance model,which follows basic mass balance equations.In general,our model agrees with commonly ex-pected hydrological responses to deforestation,con?rming the notion that potentially con?icting predictions and observations gathered by the literature do not necessarily imply inconsistency.However,because of its straightfor-wardness,it may be prudent to ?rst ask whether the model is too unsophisticated to accurately investigate such com-plex interactions.

Regarding the linear relations employed in Eqs.(3)–(5),these are clearly approximations to the actual behaviour of the water cycle in Amazonia,which does not exhibit such a strict linear dependence between ?uxes and stocks of water.However,due to the application of the constant fac-tors k 1,k 2and k 3,these quantities converge to their long-term means at steady-state.Furthermore,when moderate deviations linked to the direct effect of deforestation are imposed upon such undisturbed state of equilibrium,the system converges only to a slightly different state.Conse-quently,neither the stocks nor the ?uxes of water are al-lowed to vary signi?cantly,preventing the model to generate inconsistencies potentially caused by the approxi-mation above.Therefore,it is expected that Eqs.(3)–(5)are able to represent the low-frequency proportionality be-tween stocks and ?uxes of water with suf?cient accuracy,similarly to previous studies (Vo ¨ro ¨smarty et al.,1989).The intentional overlook of a few variables linked to the hydro-logical effects of deforestation,e.g.albedo,in?ltration and interception,is another simpli?cation requiring caution.Nonetheless,the hydrological impact of deforestation due to changes on these variables is expected to be indirectly considered by the model.Albedo,for instance,has been ob-served to increase after deforestation (Bastable et al.,1993;Roberts and Cabral,1993).Consequently,cleared soils absorb less solar radiation and thus contain less energy available to be converted in latent heat ?ux,which then must decline.Such an effect is proportional to,and also partially reproduced by,the decrease in evapotranspiration imposed in the model on every scenario of deforestation.In a similar manner,the model is also expected to have indi-rectly considered the hydrological impact due to changes in in?ltration and interception.Both of these variables have been found to decrease with deforestation (Elsenbeer et al.,1999;Godsey and Elsenbeer,2002),thus contributing to increase runoff.Therefore,the application of such parameters in the model would have only intensi?ed the re-sults encountered,since the model has predicted an in-crease in runoff over deforested areas even without considering them.Finally,the model have not considered the regrowth of deforested areas and the corresponding ef-fect on the water cycle in Amazonia.It has been docu-mented,for example,that just a few years after cutting,regenerating forests are able to produce evapotranspiration ?uxes similar to the same ?uxes over undisturbed areas (Ho ¨lscher et al.,1997;Sommer et al.,2002).However,since the totality of modeling studies considered in the present work have not taken this effect in account,we have opted to follow the exact same approach,enabling a closer comparison between the results encountered.

In any case,regardless of the acceptability of the assumptions above,it is true that our model is not able to predict the magnitude,timing,and certainly not the loca-tion of the changes with reasonable precision.However,due to its intended simplicity,it provides a fast,clear assessment of mean tendencies caused by deforestation un-der widely different scenarios,and at a reasonably ?ne spa-tial scale.More complex models,on the contrary,are capable of predicting the hydrological impact of deforesta-tion with much greater accuracy.However,due to the numerous factors and variables considered,to the coarse scale normally employed,to the uncertainties involved,and to the computational resources required,such a

broad

Figure 8Mean changes of precipitation over deforested (a)and forested (b)gridcells,as well as over the entire domain (c)as predicted by the model for the scenarios in Fig.6.Points marked with squares,circles,triangles,and ·-crosses refer to scenarios with minimum,low,high and maximum degrees of heterogeneity,respectively.

A water balance model to study the hydrological response to different scenarios of deforestation 133

assessment is presently almost impossible to perform.Still, the use of complex models is essential to con?rm the consis-tency of the results presented here and to expand their applicability.Therefore,further efforts should be directed to the development of more?exible,but yet robust models, enabling the evaluation of a wide range of scenarios of deforestation with much better accuracy.

In general,our model indicates the relevance of both scale and degree of heterogeneity of deforested areas to the overall hydrological impact generated,particularly with-in large domains such as Amazonia.It then follows that accu-rate and continuous observations of the land-cover are needed.Additionally,to facilitate the detection of the hydrological impact of deforestation in the region,the implementation of a vaster and more re?ned gauging station network is desirable.However,certain strategies for improvements on the network may be more effective than others in making the hydrological signal of deforestation sig-ni?cantly detectable at different spatial scales.In light of that,speci?c recommendations on how such improvements on the network should be pursued may be achieved with an enhanced version of our model.This version would rely on the implementation of a river networking on its scheme, and on the consideration of the ongoing geospatial structure of deforestation in Amazonia–including perhaps,a third type of gridcell referring to areas of secondary vegetation. Such proposed model framework would then allow,for example,the concomitant simulation of idealized gauging networks and projected levels of deforestation,providing a strategy for maximizing the measured response to deforesta-tion with a minimal number of additional gauging stations. Conclusions

The hydrological effects of deforestation in Amazonia seem to depend on the extent and spatial distribution of the land-surface disturbance associated.Such dependencies have been con?rmed by a few simulations performed with a grid-ded water balance model.The scenarios applied to the model follow assumptions regarding the impact of defores-tation on land–atmosphere dynamics.The only condition shared by all model experiments is a local decay(of about 10%)imposed on evapotranspiration,which is a well-known effect of deforestation.

In general,the model have showed that all water?uxes tend to decline with the size of deforestation.In the initial experiment performed,however,the model have predicted a local increase in runoff following small(<102km2)land-surface disturbances.Simulations of a widespread defores-tation(>105km2)have con?rmed the tendency for the weakening of the water cycle in the basin,especially when the mean water vapor convergence term decays.In the case of mesoscale disturbances(102–105km2),the model sug-gests that precipitation may–or,may not–get increased for early stages of deforestation(in comparison to an undis-turbed scenario),even though it also decreases as the spa-tial disturbance expands.Such a potential increase in precipitation occurs due to the spatial heterogeneity associ-ated with deforestation.The model have showed that for high levels of fragmentation,the change in the water vapor convergence?eld that follows from the intensi?cation of the horizontal heat?ux gradient between disturbed and undisturbed areas may generate an anomalous convective circulation and consequently rainfall.

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