On the spatial heterogeneity of net ecosystem productivity in ......On the spatial heterogeneity of net ecosystem productivity in complex landscapes RYAN E. EMANUEL, 1, DIEGO A. RIVEROS-IREGUI,2

On the spatial heterogeneity of net ecosystem productivityin complex landscapes

RYAN E. EMANUEL,1,� DIEGO A. RIVEROS-IREGUI,2 BRIAN L. MCGLYNN,3 AND HOWARD E. EPSTEIN4

1Department of Forestry and Environmental Resources, North Carolina State University, Raleigh, North Carolina 27695 USA2School of Natural Resources, University of Nebraska, Lincoln, Nebraska 68583 USA

3Department of Land Resources and Environmental Sciences, Montana State University, Bozeman, Montana 59717 USA4Department of Environmental Sciences, University of Virginia, Charlottesville, Virginia 22904 USA

Citation: Emanuel, R. E., D. A. Riveros-Iregui, B. L. McGlynn, and H. E. Epstein. 2011. On the spatial heterogeneity of net

ecosystem productivity in complex landscapes. Ecosphere 2(7):art86. doi:10.1890/ES11-00074.1

Abstract. Micrometeorological flux towers provide spatially integrated estimates of net ecosystemproduction (NEP) of carbon over areas ranging from several hectares to several square kilometers, but they

do so at the expense of spatially explicit information within the footprint of the tower. This finer-scale

information is crucial for understanding how physical and biological factors interact and give rise to tower-

measured fluxes in complex landscapes. We present a simple approach for quantifying and evaluating the

spatial heterogeneity of cumulative growing season NEP for complex landscapes. Our method is based on

spatially distributed information about physical and biological landscape variables and knowledge of

functional relationships between constituent fluxes and these variables. We present a case study from a

complex landscape in the Rocky Mountains of Montana (US) to demonstrate that the spatial distribution of

cumulative growing season NEP is rather large and bears the imprint of the topographic and vegetation

variables that characterize this complex landscape. Net carbon sources and net carbon sinks were

distributed across the landscape in manner predictable by the intersection of these landscape variables. We

simulated year-to-year climate variability and found that some portions of the landscape were consistently

either carbon sinks or carbon sources, but other portions transitioned between sink and source. Our

findings reveal that this emergent behavior is a unique characteristic of complex landscapes derived from

the interaction of topography and vegetation. These findings offer new insight for interpreting spatially

integrated carbon fluxes measured over complex landscapes.

Key words: carbon cycle; flux tower; Lidar; photosynthesis; respiration.

Received 24 March 2011; revised 22 June 2011; accepted 23 June 2011; published 28 July 2011. Corresponding Editor: D.

P. C. Peters.

Copyright: � 2011 Emanuel et al. This is an open-access article distributed under the terms of the Creative CommonsAttribution License, which permits restricted use, distribution, and reproduction in any medium, provided the original

author and sources are credited.

� E-mail: [email protected]

The community is a complex or mosaic of slight

irregularities, all of which blend into an entirety of

apparent homogeneity.

—Gleason 1939

INTRODUCTION

Landscapes are heterogeneous assemblages of

biotic and abiotic structures and processes

(Turner 1989). These structures and processes

interact with one another and with the external

environment and give rise to emergent behavior

and phenomena. Such emergent behavior can be

considered a key feature of aggregate complexity

(Manson 2001). Micrometeorological stations,

flumes and other observational tools are useful

for monitoring long-term physical and biological

processes over large areas (hectares to square

v www.esajournals.org 1 July 2011 v Volume 2(7) v Article 86

kilometers), but in doing so they blend the fine-scale heterogeneity of landscape processes andunderlying structures into spatially integratedvalues that may or may not reveal the underlyingcomplexity of the landscape (see recent discus-sion by Currie 2011). Spatially integrated mea-surements are valuable for assessing ecologicalprocesses at the landscape scale, but suchmeasurements can mask fundamental informa-tion regarding underlying processes and struc-tures of complex landscapes. For example, eddycovariance flux towers are powerful tools formeasuring the temporal dynamics of net ecosys-tem production (NEP) of carbon and for makingcomparisons among ecosystems, regions andbiomes because they integrate NEP over areasranging from several hectares to several squarekilometers (Law et al. 2002). However, fluxtowers are limited in their abilities to reveal theeffects of spatial heterogeneity because theyassume homogeneity of land-atmosphere (i.e.,vertical) fluxes within the footprint of the tower.

Ancillary data collected on or beneath fluxtowers are critical for interpreting temporalcontrols on NEP (Fig. 1). Additionally, measure-ments of variables such as soil CO2 efflux can

provide useful information for partitioning NEPinto constituent vertical fluxes. Even with thesecomplementary data, flux towers are generallyunable to deconvolve the spatial heterogeneity ofland-atmosphere carbon dynamics within theirindividual footprints without additional infor-mation about the spatial variability of thelandscape (Goulden et al. 1996). This informationmay or may not be necessary for simplelandscapes—those with uniform, homogeneousvegetation and essentially flat terrain, for exam-ple—where the inability of flux towers to resolvesub-footprint heterogeneity of NEP and otherfluxes may be of little concern. However, thisinformation is critical for many natural land-scapes that are neither flat nor covered uniformlyby vegetation (Baldocchi 2003).

Many natural landscapes are characterized bycomplex structures (e.g., vegetation, soil, topog-raphy, geology) that affect carbon cycle processesdirectly or indirectly and at different spatial andtemporal scales. When flux towers integratespatially over complex landscapes, they trackaverage characteristics of the ecosystem orlandscape continuously through time at sub-hourly resolution, but vital information about the

Fig. 1. Time series of two environmental variables: atmospheric vapor pressure deficit, VPD and soil water

content, SWC (top panel); daily NEP (middle panel); and cumulative NEP (bottom panel), all measured by the

Upper Stringer Creek flux tower during the 2006 growing season.


EMANUEL ET AL.

behavior of different parts of the landscape islost. To illustrate, Riveros-Iregui and McGlynn(2009) measured soil CO2 efflux at 62 locationswithin a tower-measured landscape for an entiregrowing season and found an order of magni-tude variation in the cumulative flux among thelocations. Tower-based estimates of cumulativeecosystem respiration were close to the medianvalue of cumulative soil CO2 efflux for the 62locations, but the tower itself provided noinformation about this observed range of vari-ability in the flux.

Spatially distributed models offer one solutionto the problem of lost spatial information, butmodels typically use flux tower data for tuningor verification, seeking by design to reconstructrather than leverage directly the rich temporalinformation that flux towers provide about thelandscape as a whole (e.g., Aubinet et al. 2005,Detto et al. 2006, Emanuel et al. 2010). Finer-scalecarbon flux observations within a flux towerfootprint offer another solution to this problem,but care must be taken to collect data from pointsthat span the full range of each variable thatcontributes to landscape complexity (Goulden etal. 1996). In this paper, we describe how the latterapproach can be combined with high-resolutiontopography and vegetation data from Lidar tomap tower-based NEP across a complex land-scape. Given a tower-based estimate of NEP, theframework relies on landscape variables withknown spatial distributions and known mecha-nistic links to the components of NEP to quantifythe spatial variability of NEP within a complexlandscape. In other words, we seek to character-ize the heretofore-undefined frequency distribu-tion of NEP for tower-measured landscapes.

Rather than a new mechanistic model, we areproposing a simple mathematical approach thatincorporates very basic knowledge about terres-trial carbon cycling to explain the spatial distri-bution of NEP within a complex landscape. Theframework identifies landscape positions mostlikely to function as net carbon sources or netcarbon sinks across a range of biological respons-es to climate conditions and the magnitude of thesource or sink. It also identifies positions on thelandscape most likely to transition from netcarbon sources to net carbon sinks across thesame range of biological responses. In doing so,this approach allows researchers to ask questions

including: How much spatial variability isintegrated in a flux tower estimate of NEP? Towhat degree is a constituent flux responsible forthis spatial variability? How does landscapecomplexity give rise to this spatial variability?Insight from this new method can also helpdetermine where carbon sources or sinks arelikely to be found on a specific landscape andhow climate variability can drive changes in thedistribution of sources and sinks and theirmagnitudes. Here we use the approach to gaina basic understanding of the nature and magni-tude of NEP heterogeneity in complex land-scapes.

PARTITIONING AND DISTRIBUTING NEP

We partitioned tower-based NEP into twoconstituent fluxes linked functionally to land-scape variables that can be derived from remotesensing data (e.g., Lidar). Tower-based NEP canbe expressed as

NEP ¼ GPP� RE ð1Þ

where GPP is gross primary production (i.e.,total photosynthesis of the ecosystem) and RE isecosystem respiration (i.e., the sum of allrespiration components of the ecosystem), bothintegrated over some time period (e.g., day,month, season, year). Eq. 1 is frequently appliedto one-dimensional (vertical) fluxes, which aretypically orders of magnitude larger than lateralfluxes at the ecosystem scale. Positive NEPindicates that the ecosystem is a net carbon sinkduring the integration period and negative NEPindicates that the ecosystem is a net carbonsource. Both GPP and RE carry a positive sign inthis equation; however, GPP and RE are carbonfluxes of opposite direction, typically with muchlarger magnitudes than NEP (Moncrieff et al.1996).

The components of RE can be partitioned intoaboveground and belowground respiration al-lowing Eq. 1 to be rewritten as

NEP ¼ GPP� ðRB þ RAÞ ð2Þ

where RB is belowground respiration and RA isaboveground respiration. Functionally RB com-prises root respiration and microbial decomposi-tion in soils, whereas RA comprises respirationfrom aboveground plant tissue (Chapin et al.


EMANUEL ET AL.

2002). Consequently, NEP can be partitionedamong aboveground and belowground compo-nents by restating Eq. 2 as

NEP ¼ ðGPP� RAÞ � RB ð3Þ

where GPP� RA is the aboveground componentof the land-atmosphere carbon balance and RB isits belowground component.

The aboveground land-atmosphere carbonflux (GPP � RA) cannot be measured directly atthe ecosystem level, but it can be expressedmathematically as

NPP � GPP� RA � GPP ð4Þ

since NPP (net primary production of carbon) isthe difference between GPP and all autotrophicrespiration (including aboveground and below-ground respiration). For some plant species, bothGPP and NPP increase monotonically withvegetation structural variables such as leaf areaor tree height. For example in lodgepole pine,GPP is proportional to leaf area (Lindroth et al.2008), and leaf area is correlated with tree height(Long and Smith 1988). The ratio of NPP to GPPis often constrained within a narrow range(Makela and Valentine 2001) and there is a strongcorrelation between these two fluxes for manyforest ecosystems (DeLucia et al. 2007), andespecially for lodgepole pine (Buckley andRoberts 2006), meaning that NPP can also beassumed proportional to leaf area and also to treeheight. Since NPP and GPP both increasemonotonically with leaf area and tree height,Eq. 4 suggests that GPP � RA can also berepresented by a monotonically increasing func-tion of leaf area or tree height for certain species.In other words,

GPP� RA ¼ kZb ð5Þ

where Z is a variable describing vegetationstructure (e.g., tree height), k is a constant ofproportionality, and b accounts for the nonline-arity of this relationship. Given k and b, GPP� RAcan be estimated from tree height data or otherstructural information that can be derived easilyfrom airborne Lidar (e.g., Lefsky et al. 2002,Zimble et al. 2003). One notable exception to ageneral relationship between height and GPP �RA is that in older lodgepole pines (.50 yearsold) leaf area declines even though trees continuegrowing taller, causing corresponding decreases

in GPP and NPP with loss of photosynthetictissue (Ryan and Waring 1992). In such cases, Zwould represent leaf area index instead of height.

The belowground land-atmosphere carbonflux RB is measured directly using soil CO2 effluxchambers. These chambers are commonly posi-tioned at plots distributed among experimentaltreatments or across environmental gradients onthe landscape (Scott-Denton et al. 2003, Riveros-Iregui et al. 2008). Recent work using chambermeasurements and process-based modeling hasestablished a strong relationship between cumu-lative growing season RB and topography (e.g.,uphill drainage area and aspect) due in large partto the role of topography in determining theradiation balance, soil temperature fluctuationsand the redistribution of soil water across thelandscape (Sponseller and Fisher 2008, Riveros-Iregui and McGlynn 2009, Riveros-Iregui et al.2011). For a subalpine lodgepole forest, Riveros-Iregui and McGlynn (2009) measured RB at 62soil plots across topographic gradients of uphilldrainage area and aspect and found that

RB ¼C1U þ C2; A ¼ aC3U þ C4; A ¼ b

�ð6Þ

where U is uphill drainage area, A is aspect(southward, a or northward, b), and C1 . . . C4 areempirical coefficients unique to the field site andyear. They determined C1 . . . C4 and mappedgrowing season RB at 10 m resolution for a small(3.9 km2) watershed, the boundary of whichapproximates the seasonal flux footprint of a 40m flux tower collocated at the site. This fluxtower and experimental watershed have beendescribed previously in the literature (Riveros-Iregui and McGlynn 2009, Emanuel et al. 2010).

Having determined cumulative growing sea-son RB empirically as a function of U and A forevery landscape position (e.g., Riveros-Iregui andMcGlynn, 2009), the mean value of RB for thelandscape can be determined as well. Whencombined with cumulative growing season NEPfrom a flux tower integrating the same area, Eq. 3yields the mean value of growing season GPP �RA for the entire landscape:

GPP� RAh i ¼ NEPh i þ RBh i ð7Þ

where brackets denote spatial means. ThushGPP � RAi is determined, but the spatialdistribution of GPP � RA remains unknown.


EMANUEL ET AL.

Finding the spatial distribution of GPP� RA andcombining it with the empirically derivedspatial distribution of RB is the last step indetermining the spatial distribution of NEP for acomplex landscape.

Since GPP � RA is assumed to be a functionof a vegetation height described by Eq. 5 andthe frequency distribution of Z is provided byLidar, the derived distribution approach (e.g.,Hebson and Wood 1982) provides a basis forestimating the values of k and b and therebydetermine GPP � RA as a function of Z forevery landscape position. The derived distribu-tion approach states that an unknown frequen-cy distribution Q(y) can be derived from aknown frequency distribution P(x) if y is amonotonically increasing function of x. In thiscase, the unknown frequency distribution func-tion Q(GPP � RA) can be derived from theknown distribution P(Z ) given knowledge of kand b. Coefficients k and b can be determinedfrom Eq. 5 by substituting hGPP � RAicalculated from Eq. 7 and hZi calculated fromP(Z ). Because hGPP � RAi depends on bothtower-measured hNEPi and chamber-measuredhRBi during a given growing season, validcombinations of variables k and b include afamily of power law curves that describe arange of possible vegetation behaviors for alandscape during the same growing season. Apriori knowledge of the shape of this functionalrelationship may be used to select appropriatevalues for k and b for a given species. Oncethese values have been selected, GPP � RA canbe calculated for every landscape positionwhere tree height is known. Thus, the deriveddistribution approach can be used to determineGPP � RA from Z even if the exact functionalrelationship is unknown.

Having determined GPP � RA and RB forevery position on the landscape, Eq. 3 can nowbe used to determine NEP for every landscapeposition. The mean value of the newly derivedNEP distribution is exactly equal to NEPmeasured from the flux tower. In the nextsection, we apply this framework to theforested watershed described by Riveros-Ireguiand McGlynn (2009) located at the TenderfootCreek Experimental Forest (TCEF) in Montana(US).

DISTRIBUTING NEP ACROSS A FORESTEDWATERSHED

Upper Stringer Creek is a 3.9 km2 watershedlocated at TCEF in the Rocky Mountains of west-central Montana (US). The watershed ranges inelevation from 2090 m to 2430 m and isdominated by lodgepole pine (Pinus contorta)forest (Mincemoyer and Birdsall 2006). Onaverage, TCEF receives more than 70% of its880 mm of mean annual precipitation as snow(McCaughey 1996), which melts between Apriland June, yielding a relatively steady dry-downof soils throughout the growing season (Riveros-Iregui et al. 2007). Soils throughout the water-shed are relatively shallow and uniform (Jencsoet al. 2009), and each year they transition fromrelatively wet at the beginning of the growingseason to relatively dry at the end, although notall landscape positions dry at the same rate or tothe same extent (Emanuel et al. 2010). A 40 mflux tower has measured NEP by eddy covari-ance at Upper Stringer Creek since October 2005.Fig. 1 contains a subset of data from the towersite. A full description of micrometeorologicalobservations and processing of flux data isprovided by Emanuel et al. (2010). Previousstudies have used the watershed boundary toapproximate the aggregate seasonal flux foot-print (Riveros-Iregui and McGlynn 2009, Ema-nuel et al. 2010).

In 2005, airborne Lidar measurements werecollected over approximately 50 km2 of the TCEF,including Upper Stringer Creek by the NationalCenter for Airborne Laser Mapping (NCALM,Berkeley, CA). First return (canopy top) and lastreturn (ground) elevation point data were inter-polated to 1-m2 digital elevation models (DEMs).We used the ground DEM to compute slopeaspect (A) and uphill drainage area (U) at 10 mresolution following the methods of Seibert andMcGlynn (2007), and we used the differencebetween the canopy top DEM and the groundDEM to compute tree height (Z ) at 5 mresolution following Emanuel et al. (2010). Wesubdivided A and U into 5 m 3 5 m grid cells tomatch Z. Fig. 2 shows U and Z for Upper StringerCreek as well as the location of the flux tower.

In addition to Lidar-derived spatial variables,measurements of cumulative, tower-derivedhNEPi and cumulative, chamber-derived RB are


EMANUEL ET AL.

available for the 2006 growing season (9 June–30August, 83 days total). We combined these datausing the approach described in the previoussection, determining hRBi from Eq. 6 andcombining it with hNEPi to determine hGPP �RAi. We assumed a linear relationship betweenlodgepole pine tree height and GPP� RA (i.e., b¼1), and used known values of hGPP� RAi and hZito solve Eq. 5 for k. Given k, b and the spatialdistribution of Z, we used Eq. 5 calculate GPP �RA at 5 m resolution for the entire 3.9 km

2 UpperStringer Creek watershed. Given GPP � RA andRB, we used Eq. 3 to determine NEP at 5 mresolution for the entire watershed (Fig. 3).

Having mapped cumulative growing seasonNEP for Upper Stringer Creek and determined itsfrequency distribution, three key results areevident. First, NEP is highly variable across thewatershed. The frequency distribution of NEP isnonparametric and contains both net sources andnet sinks of carbon that are very large relative totower-derived hNEPi, which was approximately270 g C m�2 for the 83-day growing season. Thefrequency distribution of NEP bears the imprintsof both the distributions of RB and GPP � RA,

illustrating in a spatially explicit fashion thenature of NEP as the difference of two opposingfluxes.

Second, the variability of NEP is highlyorganized and is a function of landscape vari-ables U and Z (Fig. 4). Note that although A isincorporated into the analysis through Eq. 6, theeffect of this variable on soil processes issecondary to U (Riveros-Iregui and McGlynn2009) and secondary to Z (Emanuel et al. 2010)for Upper Stringer Creek. That a relationshipexists between NEP and landscape variables issomewhat unsurprising since our approachassumes and is conditioned upon a prioriknowledge of the relationship between landscapevariables and carbon fluxes. However, non-intuitive patterns emerge from the intersectionof the two dominant landscape variables, U andZ. These patterns can be used to predict regionsof the landscape likely to be strong sinks orsources (i.e., combinations of U and Z that resultin relatively large positive or negative numbers)or regions of the landscape likely to shift betweensource and sink (i.e., combinations of U and Zrelatively close to 0) as factors such as climate

Fig. 2. Map of uphill drainage area, U (left panel) and tree height, Z (right panel) for the Upper Stringer Creek

watershed. Black circle shows location of flux tower and insets show frequency distributions of variables U and Z.


EMANUEL ET AL.

variability or disturbance change either thedistribution of landscape variables or the func-tional relationship between landscape variablesand carbon fluxes.

Finally, this approach, though simple in itsrepresentation of carbon dynamics, suggests thatestimates of landscape NEP and its constituentfluxes based on small-scale (e.g., 1 m2) measure-ments can be greatly biased by site selection.That landscape heterogeneity affects small-scalemeasurements has been widely recognizedacross the flux tower community (Goulden etal. 1996, Scott-Denton et al. 2003, Aubinet et al.2005); however, our approach provides a simpleprotocol for explaining how variability in small-scale measurement varies systematically across alandscape and can be predicted based onlandscape structure. For example, every locationalong the dashed line of Fig. 4 is the same valueas hNEPi measured by the flux tower. Positionsabove the line have higher-than-average NEPbecause of increased GPP � RA, decreased RB orboth. Positions below the line have lower-than-average NEP because of decreased GPP � RA,increased RB or both. Note that the meanlandscape position [hUi,hZi] produces NEP less

than hNEPi, whereas the position defined bymedian U and median Z produces NEP very

Fig. 4. Cumulative growing season NEP as a

function of U and Z. Positive NEP denotes a carbon

sink and negative NEP denotes a carbon source.

Dashed line shows all combinations of U and Z

resulting in tower-measured NEP. The open circle

shows the mean values of U and Z, and the closed

circle shows their median value. Units of NEP are g C

m�2.

Fig. 3. Maps and frequency distributions for RB (left panel), GPP� RA (middle panel) and NEP (right panel).All flux units are g C m�2.


EMANUEL ET AL.

close to hNEPi. There are relatively few landscapepositions where NEP equals hNEPi measured bythe flux tower, and the assumption that hNEPican be disaggregated into hRBi and hGPP � RAiuniformly across the landscape is clearly invalidas demonstrated by this example.

UNCERTAINTY IN THE PRODUCTIVITY-STRUCTURE RELATIONSHIP

The relationship between tree structure (e.g.,height, leaf area) and relative productivity of alandscape represented in Eq. 5 can be subject toconsiderable uncertainty depending on tree age,tree density and species, and for a givenlandscape may change from year to year as afunction of climate variability. We evaluated theeffects of the productivity-structure relationshipon the spatial heterogeneity of NEP by examininga range of values for b for the lodgepole-dominated Upper Stringer Creek watershed asan example landscape.

Equation 5 can accommodate three types offunctional behaviors: slow mathematical growth(b , 1), linear growth (b ¼ 1) and fast mathe-matical growth (b . 1). The example in theprevious section was based on linear growth (i.e.,productivity is directly proportional to treeheight for lodgepole pines). Since the value of bdetermines the sensitivity of productivity (i.e.,GPP � RA) to vegetation structure (i.e., Z ) atdifferent structural scales, we can use b as acoarse indicator of species effects, climate effectsor interactions between species and climate (e.g.,vegetation water stress). By varying b systemat-ically for a single vegetation type (here, lodge-pole pine), we can account for uncertaintyinherent in this simple approach, and moreimportantly we can begin to understand howinterannual variability in the productivity-struc-ture relationship may affect the distribution ofcarbon sources and sinks in a complex landscape.

We simulated GPP� RA and NEP for b¼ 0.5, b¼ 1 and b¼ 2 to represent the three behaviors ofEq. 5 and assess the effects of these behaviors onthe spatial distribution of GPP � RA and NEP(Fig. 5). In each case cumulative growing seasonhNEPiwas specified by the flux tower as it was inthe previous section, meaning that for a given bthere was only one possible value for k. Asexpected, in the slow mathematical growth case

lodgepole productivity is most sensitive to treeheight for smaller trees, and the sensitivitydiminishes with height. This case produces theleast spatial variability in NEP. In the fastmathematical growth case, fewer and taller treesare responsible for an increasing amount of GPP� RA. Thus, in the b ¼ 2 case, vegetation isresponsible for more of the spatial variability ofNEP than in the other two cases. Although hNEPiremains the same in each case, the distributionsof carbon sinks and NEP vary as the relationshipbetween cumulative growing season productiv-ity and vegetation structure changes. The ex-treme values of spatially distributed growingseason NEP (61000 g C m2) are not unreasonablegiven the range of growing season soil CO2effluxes observed at the site by Riveros-Ireguiand McGlynn (2009), and the range of annualGPP values modeled for different forest ecosys-tems, including another subalpine lodgepoleforest (Wang et al. 2009).

Fig. 5. Productivity-Structure relationship of Eq. 5

for three mathematical growth behaviors (top panel)

and cumulative frequency distribution of NEP result-

ing from each of the three behaviors (bottom panel).


EMANUEL ET AL.

Generalizing over a wider range of scalingbehavior (b ¼ 0 to 4), the influence of vegetationstructure on the heterogeneity of NEP becomesmore apparent (Fig. 6). When b¼ 0, every tree inthe watershed sequesters the same amount ofcarbon during the growing season (i.e., produc-tivity is uniform across the landscape). In thiscase, the spatial variability of NEP is determinedentirely by RB and its primary dependence on U.Because the frequency distribution of U isskewed (Fig. 2), approximately 60% of thewatershed has above average NEP (here ‘‘aver-age’’ is defined by the range 270 6 20 g C m�2).As cumulative growing season productivitybecomes more sensitive to tree size (i.e., as bincreases in Fig. 6), fewer trees are required tosequester the carbon necessary to offset hRBi andyield tower-measured hNEPi. Hence, for a giventower-based measurement of hNEPi, the fractionof the watershed comprising net sinks decreasesas the magnitude of each remaining sink grows

larger. A real-life scenario that corresponds tothis case could be an extremely dry year, inwhich taller trees with more root biomass anddeeper root penetration with subsequently moreaccess to water than shorter trees sequester amajority of the carbon and contribute dispropor-tionally to hNEPi.

Simulating the effects of interannual climatevariability by varying b also reveals three distinctregimes of hNEPi behavior (Fig. 7). First, someparts of the landscape remain carbon sinksregardless of how sensitive productivity is totree height. For Upper Stringer Creek, theseregions comprise relatively tall trees on relativelydry hillslopes. Modeling by Emanuel et al. (2010)suggests that for the relatively dry 2006 growing

Fig. 6. Fraction of watershed having above average

or below average hNEPi as a function of b (above) andfraction of watershed comprising net sources or sinks

as a function of b (below).

Fig. 7. Perpetual carbon sinks (light gray) and

perpetual carbon sources (dark gray) over the range

b ¼ 0 to 4 as a function of U and Z (top panel) andmapped for Upper Stringer Creek (bottom panel).

Color gradient represents likelihood of carbon sinks

for transitional landscape positions (i.e., those that

move from net sinks to net sources as b increases).


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season, trees in these landscape positions expe-rienced water stress, but not to the extent thatstomatal conductance was drastically reduced.We assume this to indicate that tree height is stilla valid first-order control on GPP � RA, evenwhen feedbacks from drier topographic positionsare considered. Second, other parts of thelandscape always remain carbon sources. Theycomprise relatively short trees on lower hillslopepositions where abundant soil moisture persistslater into the growing season (subsidized bydrainage from upslope areas), facilitating RB.Trees at these landscape positions have access torelatively abundant soil moisture, but theirsmaller structures limit their capacity to seques-ter carbon compared to larger trees with morephotosynthetic tissue. Third, some areas of thelandscape transition from source to sink (or viceversa) from year to year depending on therelationship between productivity and structure.These areas tend to be characterized by interme-diate values of landscape variables U and Z, andthe constituent fluxes GPP � RA and RB are ofsimilar magnitude. Changing the sensitivity ofhNEPi to one of the landscape variables throughclimate mediated processes can tip the balanceand cause these landscape positions to functionas either net sources or net sinks of carbon.

That these distinct regimes (i.e., perpetualsinks, perpetual sources and transitional areas)exist may be intuitive, but their pattern on thelandscape is non-intuitive. The spatial patternbears the unique imprint of our field site, UpperStringer Creek, but it also provides generalinsight about the ability of the NEP distributionto change from year to year. Specifically, theexistence of a relatively large transitional zonecharacterized by intermediate topography andvegetation suggests that in these areas year toyear climate variability may be the primaryfactor determining whether a landscape positionfunctions as a carbon source or a sink. Incontrast, areas that are perpetual carbon sourcesor sinks owe their source/sink status primarily tothe intersection of topographic and vegetationstructure rather than to interannual climatevariability, although climate variability maystrongly influence the magnitude of the sourceor sink from year to year. In the absence ofvegetation disturbance or successional change(which effectively alter the spatial distribution of

Z ), the source/sink status of some areas (perpet-ual sources and sinks) is solely a function ofspatial pattern (topography and vegetation at agiven position), but the source/sink status oftransitional areas is a function of both spatialpattern and temporal dynamics. For the land-scape as a whole, hNEPi is thus defined by the co-organization of topographic and vegetationvariables on the landscape and also by climaticinfluence on the relationship between spatialvariables and constituent fluxes of hNEPi. Theexistence of different NEP regimes in the samecomplex landscape may help to explain why it issometimes difficult to interpret the response oftower-integrated NEP to environmental variables(e.g., Fig. 1).

Landscapes lacking complex topography, veg-etation or both may contain only one or two ofthe regimes because, spatially, they have fewerdegrees of freedom than represented in Fig. 7.For example, uniform vegetation on flat terraincould be represented as a single point in the U�Z phase space. Depending on the specificfunctional responses of its constituent carbonfluxes, it could be situated in any of the threeregimes and exhibit source, sink or transitionalbehavior. As long as the vegetation remainsuniform, it will remain a single point in thephase space, but it will migrate in the Zdimension each year as vegetation structurechanges. This example and the preceding exam-ples only consider year-to-year variability of theGPP� RA distribution; additional work is neededto understand (1) how the distribution of RBchanges from year to year in response to climateand (2) how vegetation disturbance and succes-sional dynamics affect the climate-mediateddependence of GPP � RA on Z.

These results suggest that the degree oflandscape complexity determines, in part, wheth-er or not carbon sinks, carbon sources andtransitional regimes exist or co-exist in a givenlandscape. Landscapes with complex topograph-ic and vegetation structures (e.g., Upper StringerCreek) provide sufficient heterogeneity to sup-port all three regimes. For Upper Stringer Creek,we define landscape complexity using two mainvariables, uphill drainage area and tree height.Other landscapes may derive complexity fromdifferent topographic variables (e.g., large eleva-tion gradients, high degree of slope variability),


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different vegetation variables (e.g., differences inspecies or functional types, density of vegeta-tion), or additional sources (e.g., soil physical orchemical characteristics, natural or human dis-turbance). Landscapes that lack recognizablecomplexity in topography, vegetation and/orother variables have fewer spatial degrees offreedom and may be less likely (if at all) tocontain multiple regimes. Thus, interactions ofheterogeneous landscape variables and the bio-physical processes with which these variables areassociated are responsible not only for the spatialdistribution of NEP, but also for the emergence ofmultiple NEP regimes within a landscape. UpperStringer Creek illustrates the potential for multi-ple regimes to coexist within a single complexlandscape, but we posit that this emergentbehavior is a general phenomenon and can beconsidered a defining characteristic of all com-plex landscapes.

CONCLUSION

We have presented a simple approach fordistributing cumulative growing season NEPacross a complex landscape. The approachrequires knowledge of the spatially integratedNEP (e.g., from a flux tower), and it requiresspatially distributed information about vegeta-tion and topographic structure for the landscape(e.g., from Lidar). The approach also requiresthat a relationship between soil CO2 efflux andtopographic structure exists and is known. Arelationship between productivity and vegetationstructure is assumed to exist as a monotonicallyincreasing function, but its exact form need notbe known to determine the spatial distribution ofproductivity and NEP.

We demonstrated that the spatial distributionof cumulative growing season NEP bears theimprint of the spatial variables that influencebiophysical processes within a complex land-scape. We also demonstrated that considerablespatial heterogeneity may underlie tower-inte-grated measurements of NEP, but there isstructure and organization to this heterogeneitythat facilitates prediction of net carbon sourcesand sinks within the landscape. These resultssuggest that uniform partitioning of NEP intoconstituent fluxes is not appropriate acrosscomplex landscapes.

When we simulated year-to-year climate var-iability by varying the relationship betweenvegetation structure and productivity, we foundthat complex landscapes fostered three distinctbehavioral regimes: some areas of the landscapewere perpetual carbon sinks, some areas wereperpetual carbon sources, and some areas tran-sitioned between sink and source depending onthe vegetation response to climate. This can beconsidered a defining characteristic of complexlandscapes that emerges through the interactionof topography and vegetation. The behavior ofspatially distributed NEP in simpler landscapescould be described as a special case of complexlandscapes with fewer spatial degrees of free-dom. Analyses of spatially integrated fluxes overcomplex landscapes should consider the spatialheterogeneity of fluxes and whether their distri-butions across the landscape could have animpact on interpretations and conclusions drawnfrom these data.

ACKNOWLEDGMENTS

This work was funded in part by the Department ofForestry and Environmental Resources at NorthCarolina State University and by NSF awards EAR-0404130, EAR-0837937 and DEB-0807272. Additionalsupport was provided by the AGU Horton ResearchGrant awarded to Dr. Riveros-Iregui. Airborne Lidarwas provided by the NSF-supported National Centerfor Airborne Laser Mapping (NCALM) at the Univer-sity of CA, Berkeley. We are grateful to Robert E. Keaneand Elaine Sutherland of the USDA Forest ServiceRocky Mountain Research Station, Tenderfoot CreekExperimental Forest for site access and logisticalsupport. Paolo D’Odorico provided valuable feedbackon the mathematical approach and two anonymousreviewers provided insightful suggestions to strength-en the paper.

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