Landscape Ecology vol. 9 no. 4 pp 249-260 (1994) SPB Academic Publishing bv, The Hague Response of North American ecosystem models to multi-annual periodicities in temperature and precipitation J. Alan Yeakley 1 '*, Ron A. Moen 2 , David D. Breshears 3 '** and Martha K. Nungesser 4 ; Institute of Ecology, University of Georgia, Athens, GA 30602 USA; 2 Department of Fisheries and Wildlife, University of Minnesota, St. Paul, MN 55108 USA; 3 Environmental Science Group, Los Alamos National Laboratory, Los Alamos, NM 87545 USA; and Department of Radiological Health Sciences, Colorado State University, Fort Collins, CO 80523 USA; 4 Department of Environmental Sciences, University of Virginia, Charlottesville, VA 22903 USA Keywords: Climate cycles, forest ecology, grassland ecology, gap models, STEPPE, LINKAGES, time series analysis, frequency analysis Abstract Ecosystem models typically use input temperature and precipitation data generated stochastically from weather station means and variances. Although the weather station data are based on measurements taken over a few decades, model simulations are usually on the order of centuries. Consequently, observed periodicities in temperature and precipitation at the continental scale that have been correlated with large- scale forcings, such as ocean-atmosphere dynamics and lunar and sunspot cycles, are ignored. We investi- gated how these natural climatic fluctuations affect aboveground biomass in ecosystem models by incorporat- ing some of the more pronounced continental-scale cycles in temperature (4, 11, 80, 180 year periods) and precipitation (11 and 19 year periods) into models of three North American forests (using LINKAGES) and one North American grassland (using STEPPE). Even without inclusion of periodicities in climate, long-term dynamics of these models were characterized by internal frequencies resulting from vegetation birth, growth and death processes. Our results indicate that long-term temperature cycles result in significantly lower predictions of forest biomass than observed in the control case for a forest on a biome transition (northern hardwoods/boreal forest). Lower-frequency, higher-amplitude temperature oscillation caused amplification of forest biomass response in forests containing hardwood species. Shortgrass prairie and boreal ecosystems, dominated by species with broad stress tolerance ranges, were relatively insensitive to climatic oscillations. Our results suggest periodicities in climate should be incorporated within long-term simulations of ecosystems with strong internal frequencies, particularly for systems on biome transitions. Introduction Agren et al. 1991; Kienast 1991; Rastetter et al. 1991). Output response depends both on the func- Models of terrestrial ecosystems have been used tions within the models and on the functional for- primarily to understand long-term responses of mat of the input (e.g., temperature and precipita- large systems to both static and changing environ- tion) data. While the level of complexity of internal mental conditions (Shugart and West 1977; Davis mechanisms is continually being refined (e.g., and Botkin 1985; Pastor and Post 1986, 1988; Run- Smith and Urban 1988; Friend et al. 1993; Lauen- ning and Coughlan 1988; Overpeck et al. 1990; roth et al. 1993), representation of input data is * Current address: Department of Environmental Sciences, Portland State University, Portland, OR 97207 USA ** Address for correspondence: Environmental Sciences Group, Mail Stop J495, Los Alamos National Laboratory, Los Alamos, NM 87545 USA
Response of North American ecosystem models to multi-annual
periodicities in temperature and precipitation
J. Alan Yeakley1'*, Ron A. Moen2, David D. Breshears3'** and Martha K. Nungesser4
; Institute of Ecology, University of Georgia, Athens, GA 30602 USA; 2 Department of Fisheries andWildlife, University of Minnesota, St. Paul, MN 55108 USA; 3 Environmental Science Group,Los Alamos National Laboratory, Los Alamos, NM 87545 USA; and Department of RadiologicalHealth Sciences, Colorado State University, Fort Collins, CO 80523 USA; 4 Department ofEnvironmental Sciences, University of Virginia, Charlottesville, VA 22903 USA
Keywords: Climate cycles, forest ecology, grassland ecology, gap models, STEPPE, LINKAGES, timeseries analysis, frequency analysis
Abstract
Ecosystem models typically use input temperature and precipitation data generated stochastically fromweather station means and variances. Although the weather station data are based on measurements takenover a few decades, model simulations are usually on the order of centuries. Consequently, observedperiodicities in temperature and precipitation at the continental scale that have been correlated with large-scale forcings, such as ocean-atmosphere dynamics and lunar and sunspot cycles, are ignored. We investi-gated how these natural climatic fluctuations affect aboveground biomass in ecosystem models by incorporat-ing some of the more pronounced continental-scale cycles in temperature (4, 11, 80, 180 year periods) andprecipitation (11 and 19 year periods) into models of three North American forests (using LINKAGES) andone North American grassland (using STEPPE). Even without inclusion of periodicities in climate, long-termdynamics of these models were characterized by internal frequencies resulting from vegetation birth, growthand death processes. Our results indicate that long-term temperature cycles result in significantly lowerpredictions of forest biomass than observed in the control case for a forest on a biome transition (northernhardwoods/boreal forest). Lower-frequency, higher-amplitude temperature oscillation caused amplificationof forest biomass response in forests containing hardwood species. Shortgrass prairie and boreal ecosystems,dominated by species with broad stress tolerance ranges, were relatively insensitive to climatic oscillations.Our results suggest periodicities in climate should be incorporated within long-term simulations of ecosystemswith strong internal frequencies, particularly for systems on biome transitions.
Introduction Agren et al. 1991; Kienast 1991; Rastetter et al.1991). Output response depends both on the func-
Models of terrestrial ecosystems have been used tions within the models and on the functional for-primarily to understand long-term responses of mat of the input (e.g., temperature and precipita-large systems to both static and changing environ- tion) data. While the level of complexity of internalmental conditions (Shugart and West 1977; Davis mechanisms is continually being refined (e.g.,and Botkin 1985; Pastor and Post 1986, 1988; Run- Smith and Urban 1988; Friend et al. 1993; Lauen-ning and Coughlan 1988; Overpeck et al. 1990; roth et al. 1993), representation of input data is
* Current address: Department of Environmental Sciences, Portland State University, Portland, OR 97207 USA** Address for correspondence: Environmental Sciences Group, Mail Stop J495, Los Alamos National Laboratory, Los Alamos,NM 87545 USA
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typically relegated to simple stochastic equationsbased on means and variances in climate data.There are at least two problems with this approach:(1) ecosystem models are typically run on timescalesthat exceed the length of the original input climatedata series by at least an order of magnitude, and(2) it ignores climate studies (Michaels and Hayden1987; Stocker and Mysak 1992) that have demon-strated that significant deterministic fluctuation ex-ists in climate variables at frequencies relevant tointernal cycles resulting from birth, growth anddeath processes of vegetation dynamics (Shugart1984; Neilson 1986).
Background
Periodic behavior in precipitation and temperatureseries has been observed at a variety of spatial andtemporal scales. Naturally-occurring frequencieshave been attributed to the El Nino-Southern Oscil-lation (ENSO) (2-10 years), sunspot and double-sunspot cycles (11 and 22 years), and the lunar cycle(18.6 years), as well as other longer cycles (> 40years) which have explanations ranging from ex-tended sunspot cycles to ocean-atmosphere interac-tions (Stocker and Mysak 1992, Burroughs 1992).For example, a lunar cycle with a period of about19 years has been reported from rain-gauge recordsof the western U.S. (Kerr 1984; Currie and O'Brien1990). Sunspot and double-sunspot cycles havebeen correlated with drought cycles based on tree-ring data and rain-gauge records (Vines 1982; Cur-rie and O'Brien 1990). Data from ice cores in north-ern Canada contained three main frequencies inprecipitation, two of which were attributed to sun-spot and double-sunspot cycles, and a third with aperiod of 3.8 yrs that may correspond with an ElNino cycle (Holdsworth et al. 1992). Estimated am-plitude for these cycles is in the range of 5-10% ofannual mean precipitation (Vines 1982; Currie andO'Brien 1988).
Cycles in annual temperature have also beenreported, although these are more variable. Perio-dicities from 10 to 100 years in mean annual tem-perature were reported by Wigley and Raper(1990). Broecker (1975) found 80 and 180 year peri-ods of global temperature based on 1000 years of
ice-core data. A ten year periodicity in temperaturewith an amplitude of about 0.6°C approximatingthe periodicity of a sunspot cycle was reported byJones et al. (1986). Recent studies have linked solarcycle variability with terrestrial temperature re-sponse (Kelly and Wigley 1992; Schlesinger andRamankutty 1992; Rind and Overpeck 1993; Leanand Rind 1994). Investigating temperature responseto ENSO events from 1880 to 1984, Ropelewski andHalpert (1986) found ENSO events occurring every2 to 10 years. Quinn and Neal (1992) reported amean 3.9 year period for ENSO from the historicalrecord since 1526. Oscillation ranges of the longercycles (> 50 year) were as much as 4°C (Broecker1975), while oscillation ranges of shorter cyclestended to be less than 1 °C (Jones et al. 1986; Wigleyand Raper 1990). In a recent review, Stocker andMysak (1992) proposed ocean-atmosphere interac-tions as a possible cause for cycles with periodsranging from 50 to 400 years. While the occurrenceof periodicities is thus well documented, causallinks remain unclear except in the case of the ENSO(Mitchell 1976, Enfield 1989, Burroughs 1992).
Climatic inputs in ecosystem models primarilygovern rates and limit the extent of processes. Tem-perature affects process rates in vegetation models,particularly the rates of photosynthesis, carbon al-location, respiration and decomposition (Agren etal. 1991; Lauenroth et al. 1993). Water availabilitycan limit photosynthesis through its effect onstomatal conductance (Agren et al. 1991), or canaffect regeneration and mortality probabilities(Pastor and Post 1985; Coffin and Lauenroth1990). Although these external variables constrainthe possible response of internal model variablessuch as biomass, the nonlinear nature of biologicalfunctions can lead to unexpected responses to vari-ations and trends in climate constraints, particular-ly near critical endogenous thresholds (Shugart etal. 1980; O'Neill et al. 1989). Even small changes inan external variable such as temperature have beenshown to result in significant shifts in biomass andavailable soil nitrogen in simulations of a forestecosystem (Cohen and Pastor 1991).
Attributes of terrestrial ecosystems such as bio-mass can contain internal frequencies which cor-respond to synchronous demographic processes,e.g., birth-death cycles, growth spurts due to com-
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petitive release, and dieback resulting from pres-sures such as climate or herbivory (Shugart 1984;1987; Neilson 1986; Urban et al. 1987). Suchecosystems are thus inherently nonlinear; so analy-sis of general ecosystem responses to a suite of inputstructures is not straightforward (DeAngelis andWaterhouse 1987). Yet, some techniques fromlinear systems analysis, such as frequency analysis,can be applied to evaluate responses of nonlinearsystems (Emanualet al. 1978; Shugart 1984). Mod-els are filters that, depending on their internal struc-ture (e.g., connectivity, component process rates),pass, attenuate and/or amplify signals dependingon input frequency (Brown 1983; O'Neill et al.1986; DeAngelis et al. 1986). Modification of out-put can occur when an input signal occurs eithersynchronously with a dominant internal model fre-quency resulting in signal amplification (i.e., re-sonance) or desynchronously with internal frequen-cies resulting in attenuation of a model output sig-nal. Gosz and Sharpe (1989) have discussed suchsignal modifications in the context of biome transi-tions, hypothesizing that vegetation in such areaswould be very responsive to changing environmen-tal constraints due to the mixture of lifeforms (e.g.,grasses, shrubs, trees) with different structuralcharacteristics. In comparing the dynamics of agrassland and a forest, Coffin and Urban (1993)found that response to cyclic variation in availablemoisture was associated with differences in life his-tory traits. The forest responded strongly to a singlefrequency corresponding to the lifespan of thedominant species, while the grassland composed ofperennial plants with clonal growth exhibited aweaker response at all frequencies of the externalconstraint.
Michaels and Hayden (1987) have called formore realistic representation of climate in eco-system models, emphasizing the non-random na-ture of climatic processes. The standard stochasticapproach does not account for acute disturbanceevents (e.g. hurricanes) or long-term climateanomalies (e.g. protracted drought), both of whichmay result in species-specific response thresholdsbeing reached or exceeded. Currently regional- andcontinental-scale ecosystem and biome models arebeing developed to assess the response of the bio-
sphere to climatic variability and change (Burke etal. 1991; Neilson etal. 1992;Lauenrothe/a/. 1993).The adequacy of ecosystem models, particularlygap models, to represent climate change effects hasbeen under recent scrutiny (Bonan and Sirois 1992;Weinstein 1992).
Approach
Our primary objective was to determine the effectof known periodicities of climate in inputs to terres-trial ecosystem models, as opposed to modeling cli-mate simply as stochastic variation about a long-term mean. We modeled four ecosystem types inNorth America, ranging from shortgrass prairie toboreal forest to eastern deciduous hardwoods. Weselected well-documented temperature and precipi-tation cycles that are relevant on a continental scalefor North America and expected to be temporallyrelevant for these models. The cycles were chosen tobe representative rather than exhaustive, spanningtimescales from sub-decadal to multi-century(Table 1).
Methods and analyses
Study sites and models
We selected one grassland and three forestecosystems in which to study sensitivity to cyclicalclimate inputs. Forest ecosystems included a borealforest in Ontario (49°N, 82°W), a forest compris-ing a transition from boreal to northern hardwoodsin Minnesota (47°N, 92° W), and an eastern decidu-ous hardwood forest in Tennessee (35°N, 86°W).The grassland system was a shortgrass prairie innorthcentral Colorado (41 °N, 108°W) dominatedby blue grama (Bouteloua gracilis).
All three forest ecosystems were modeled usingLINKAGES, a forest growth model developed foreastern North America (Pastor and Post 1985,1986) from the JABOWA/FORET family of gap-based forest dynamics models (Botkin et al. 1972;Shugart and West 1977). Gap models simulaterecruitment, growth and mortality of individual
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Table 1. Temperature and precipitation periodicities used in the simulations.
TemperaturePeriod
4 yrs
11 yrs80 yrs
180 yrs
PrecipitationPeriod
11 yrs19 yrs
Amplitude0.6°C
0.6°C1.2°C1.2°C
Amplitude.075*Mean.075*Mean
ReferencesRopelewski and Halpert 1986, Holdsworth
et al. 1992, Quinn and Neal 1992Jones et al. 1986, Wigley and Raper 1990Broecker 1975, Stacker and Mysak 1992Broecker 1975, Stocker and Mysak 1992
ReferencesVines 1982, Currie and O'Brien 1988, 1990Kerr 1984, Currie and O'Brien 1988, 1990
plants on a single plot through time, with plot sizecorresponding to the size of a mature dominant in-dividual plant in the ecosystem. Trees growing onmodel plots compete for available light, water andnutrients under varying temperature constraints.Recruitment and mortality are simulated asstochastic processes while growth is deterministic.Species-specific input data such as plant growthcharacteristics and litter decomposition parameterswere as reported in Pastor and Post (1985). Soiltype for all forests was standardized to a loam hav-ing a field capacity of 28.0% and a wilting point of13.3% (Pastor and Post 1985).
The shortgrass prairie was simulated using thegap-based model STEPPE (Coffin and Lauenroth1990; Lauenroth et al. 1993; Coffin and Urban1993). In contrast to the forests, the most intensecompetition in semi-arid grasslands is assumed tooccur below ground. Growth is a function of tem-perature, precipitation, and interactions with otherplants in the plot. Regeneration and mortality aredriven by annual precipitation. Two importantdifferences exist between STEPPE and LINK-AGES. The timestep of LINKAGES is monthlywhereas that for STEPPE is annual. Soil moistureand nitrogen dynamics are explicitly included inLINKAGES; by contrast, these resources arelumped into a 'resource abundance curve' con-trolled by annual precipitation in the version ofSTEPPE used here (Coffin and Lauenroth 1990).
Climatic Input
Temperature and precipitation are computedstochastically in LINKAGES and STEPPE by ad-ding a normally distributed random deviate to along-term mean at each timestep. Variance used incomputing the random component is based onmeteorological datasets that are typically 30 yearsin length. To simulate cyclic patterns in tempera-ture and precipitation, we modified this computa-tion with a sine wave component:
where T; and P; are mean temperature and precipi-tation, respectively, for time i, A is amplitude, Y iscurrent year in the model run, H is horizontal shift,L is period of the climate cycle simulated, andNti(t) and N .(t) are normal deviates computedfrom the variance in temperature and precipitationdata, respectively, for time i.
For the simulations, we used initialization peri-ods from 500 to 750 years for forest systems and200 years for grassland systems. Such periods werenecessary to overcome transient model responsesdue to model runs starting on bare ground. Theseinitialization periods were determined from pre-liminary model runs (Emanuel et al. 1978; Shugartand West 1981; Coffin and Lauenroth 1990).Amplitudes and frequencies for temperature andprecipitation cycles were selected to represent someof the more predominant climate signals and to span
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as many orders of magnitude as we thought likelyto be relevant to the internal frequencies of the eco-system simulated (Table 1). We selected the hori-zontal shift, H, such that it would equal zero at theend of the initialization period to standardize timingof cyclic behavior among runs. From that point, wecollected model biomass estimates for at least 1500years for each model run. The longest importantperiod previously reported for gap models is 200—250 years (Emanuel et al. 1978). Thus we collecteddata for more than four times the length of thelongest period, as suggested by Jassby and Powell(1990). Each resulting time series then was de-trended by performing a linear regression and usingthe residuals as the resulting data series.
Analysis
Difference in biomass between the mean of 30 plotsfor the control run and 30 plots for a given treat-ment run (Table 1) for each simulated ecosystemwas determined using a two sample t-test (p = 0.01;Zar 1984, p. 126) for each year for 1500 years fol-lowing the initialization period (for a given year,plots in all model runs are independent). Theproportion of years either significantly low or highcompared to the control case was tabulated to dis-play the long-term effect of a given treatmentscenario on biomass. Frequency analysis was usedto determine dominant cycles in model biomass un-der various input scenarios (Platt and Denman1975; Emanuel et al. 1978). This analysis providedan objective basis for comparing biomass responsebetween control and cyclic input at each site, as wellas among different sites for each input scenario.Power spectral density functions (SAS/ETS 1982)were generated for the biomass residual time seriesfor each of the climate scenarios at each site. White-noise tests (Fisher's Kappa, Kolmogorov-Smirnov)were conducted to determine if the biomass timeseries in each case could be distinguished from a ser-ies randomly distributed in time. For 1500 observa-tions, critical values showing significant periodicityat p < 0.01 were: Fisher's Kappa > 12.0 andKolmogorov-Smirnov statistic > 0.042 (Fuller1976).
Results
White-noise tests showed that significant non-random periodicities in aboveground biomass exist-ed in all ecosystems simulated, even for all controlscenarios (i.e., random climate). This indicates thatall systems contained internal frequencies, regard-less of climatic input. For control scenarios, Fish-er's Kappa values were 44.7 for shortgrass prairieand at least an order of magnitude higher than thecritical value for all forest ecosystems. Similarly,Kolmogorov-Smirnov statistics for control caseswere 0.5 for the shortgrass prairie and from0.84-0.91 for the forest systems. Generally,strength of non-random periodicities as indicatedby white noise tests increased in the order: Short-grass prairie < Boreal forest = Eastern hardwoods< Northern hardwoods/boreal transition forest.
Precipitation treatments produced no pronounc-ed differences in biomass for any of the ecosystems(Fig. 1). Grassland biomass was relatively unaffect-ed by differences in temperature input (Figs. 2a,3a). Biomass in the boreal forest was similarly un-affected (Figs. 2b, 3b). Generally, hardwood forestbiomass was most affected by differences in tem-perature cycles, with lower-frequency and higher-amplitude temperature oscillations (80 or 180 yearperiod with 1.2°C amplitude) causing markedresponses (Figs. 3c, d). The simulated transitionalforest (boreal/northern hardwoods) showed a largedrop in biomass for lower-frequency, higher-ampli-tude scenarios (Fig. 3c).
Mean biomass remained constant for all scena-rios except for low-frequency temperature cycles inthe Minnesota transition forest (Table 2). Biomassshowed greater variation for lower-frequency,higher-amplitude cycles both in the eastern hard-woods and in the boreal/northern hardwood transi-tion forest. The proportion of years in which meantreatment biomass differed from mean control casebiomass significantly at the p = 0.01 level showedthe same pattern, with the greatest significantlydifferent proportions occurring for the mixed tran-sition forest and for the eastern hardwood forest.Low-frequency, high-amplitude oscillation result-ed in decreased mean biomass in the transitionforest relative to the control case, while in the
254
(a) Shortgrass prairie
g/m 2 150 •• • • • JL- ' 1 . 'nW <!'•>,jUsK ./.;: re .'rtL* A ;:v.:L (A
1500 1550 1GOO(b) Boreal forest
Mg/ha 150100501800 1850 1BOO 1050
(c) Boreal / Northern hardwoods
Mg/ha 250
]0 1850 1((d) Eastern hardwoods
Mg/ha
1850 1000 1050Simulation year
control 11 year ppt. cycle 19 year ppl. cycle
Fig. 1. Simulated biomass of four ecosystems in response to cli-matic functions for precipitation for a 200-year time interval fol-lowing model initialization. Complete model runs were for atleast 1500 years following initialization. Simulations are controlplus treatments of 11 year and 19 year precipitation cycles; eachsimulation included random variability in precipitation. Simu-lated ecosystems, from top to bottom, are (a) shortgrass prairie,(b) boreal forest, (c) boreal/northern hardwoods transitionforest, and (d) eastern hardwoods.
boreal and eastern hardwood forest mean biomasswas not different among treatments and controlcase (Fig. 3, Table 2).
Grassland spectral density estimates varied some-what (Fig. 4a, e) under both different precipitationand temperature input structures. Forest systems(Figs. 4b-d, 4f-h) showed striking differences,however, both among sites and among input struc-ture scenarios, particularly with respect to tempera-ture. Generally, high-frequency temperature andprecipitation input structures attenuated biomassresponse as indicated by reductions in the spectral
Simulation year—;— control 4 year temp, cycle 11 year temp, cycle
Fig. 2. Simulated biomass of four ecosystems in response toshorter-term climatic functions for temperature for a 200-yeartime interval following model initialization. Complete modelruns were for at least 1500 years following initialization. Simula-tions are control plus treatments of 4 year and 11 year tempera-ture cycles; each simulation included random variability in tem-perature. Simulated ecosystems, from top to bottom, are (a)shortgrass prairie, (b) boreal forest, (c) boreal/northern hard-woods transition forest, and (d) eastern hardwoods.
density estimates. In contrast, low-frequency tem-perature cycles tended to amplify biomass re-sponses. Amplification of biomass response fromlow-frequency climate drivers increased movingsouthward from boreal forest through mixed hard-woods to oak-hickory hardwood forest (Figs.4f-h).
Discussion
Our approach allowed us to make a broad compari-son using a common variable, annual aboveground
Fig. 3. Simulated biomass of four ecosystems in response tolonger-term climatic functions for temperature for a 200-yeartime interval following model initialization. Complete modelruns were for at least 1500 years following initialization. Simula-tions are control plus treatments of 80 year and 180 year temper-ature cycles; each simulation included random variability in tem-perature. Simulated ecosystems, from top to bottom, are (a)shortgrass prairie, (b) boreal forest, (c) boreal/northern hard-woods transition forest, and (d) eastern hardwoods.
biomass, across several contrasting systems. Theindividual-based models used here are hierarchical-ly structured (Shugart 1984; Urban et al. 1987;Shugart and Urban 1989) and so provide a multi-level depiction of response to various inputscenarios. Multi-level analysis allows determina-tion of underlying mechanistic causes whichproduce upper-level responses (Allen et al. 1984).Interpretation of an upper-level pattern can lead tomisinterpretation unless lower-level mechanismsare evaluated (Cale et al. 1989; Yeakley and Cale1991). In a hierarchical sense, annual biomass is an
upper level ecosystem attribute. The main focus ofour discussion is species-level mechanisms whichproduced system-level biomass responses to varioustypes of climatic forcing.
We found that simulated forest systems weremore strongly affected by periodic climate signalsthan the simulated grassland system. In the grass-land, only precipitation cycling exerted any amplifi-cation on the biomass signal, at approximately a110-120 year lag (Fig. 4a). The relative insensitivi-ty of the shortgrass prairie to the induced climaticperiodicities is related to the climatic tolerance ofthe dominant species, blue grama (Bouteloua graci-lis), and the high level of climatic variability inher-ent in the system even when climatic periodicitiesare ignored. The mortality function for blue gramais not dependent on a maximum age (Coffin andLauenroth 1990), as it is for trees modeled in LINK-AGES (Pastor and Post 1985). Thus, there is lesscycling of biomass inherent within the grasslandmodel in comparison with the forest models. Bluegrama has a shallow root distribution and is able torespond rapidly to small precipitation events (Salaand Lauenroth 1982, Coffin and Lauenroth 1991).These small events make up a significant propor-tion and a less variable amount of annual precipia-tion (Sala et al. 1992). As a result, blue grama is mo-deled as being relatively insensitive to changes inannual precipitation (Coffin and Lauenroth 1990).Also, the amplitudes of the continental-scale perio-dicities we implemented are relatively small com-pared to the variance in precipitation (i.e., ampli-tude of the periodicity was 7.5% of the mean vs.coefficient of variation for annual precipitationwas 25.6%). Temperature is assumed to influencethe rate of growth of blue grama but not regenera-tion probability (Coffin and Lauenroth 1990). Inconcert these factors suggest biomass dynamics inthe shortgrass prairie should be relatively insensi-tive to the continental scale periodicities in climatereported in the literature.
In contrast, forest systems showed substantial bi-omass responses, both in terms of amplificationand attenuation, to precipitation and temperatureoscillations. The boreal ecosystem was the leastresponsive forest, showing a minimal reponse toprecipitation cycling (Figs. Ic, 4b) and an amplified
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Table 2. Long-term differences in biomass. Data used were from the last 1500 years of each simulation. Treatment mean was comparedto control mean at a p = 0.01 significance level for each year. Shown is proportion of all years for which a significant difference wasfound. Treatments are indicated by P for precipitation and T for temperature cycles, followed by period of cycle (yrs).
Shortgrass prairie
ControlP - 11P - 19T - 4T - 11T - 80T - 180
Boreal forest
ControlP - 11P - 19T - 4T - 11T - 80T - 180
Mean[g/m2]143.5144.1143.9143.0142.9144.1144.1
Mean[Mg/ha]136.1136.6135.0135.9137.4134.5133.2
Std Dev[g/m2]5.76.36.06.05.56.16.6
Std Dev[Mg/ha]7.78.26.99.26.88.29.5
Sig Low[%]-232227272424
Sig Low[%]-283432223440
Non-sig[%]-495251515048
Non-sig[%]-443842484135
Sig High[%]-282522232628
Sig High[%]-282827312525
Boreal /Northern hardwoods
ControlP - 11P - 19T - 4T - 11T - 80T - 180
Eastern hardwoods
ControlP - 11P - 19T - 4T - 11T - 80T - 180
Mean[Mg/ha]310.0316.2314.4300.7303.6184.2222.0
Mean[Mg/ha]242.9240.5243.1243.4242.5238.8242.5
Std Dev[Mg/ha]18.013.313.111.117.832.344.4
Std Dev[Mg/ha]14.713.814.713.29.5
20.640.6
Sig Low[%]-242744439993
Sig Low[%]-342525303943
Non-sig[%]-32283731
14
Non-sig[%]-42
.4746413311
Sig High[%]-4445192703
Sig High[%]-252830292845
response to only the lowest frequency (180 yearperiod) temperature fluctuation (Fig. 4f). The lackof sensitivity of boreal forest biomass to climaticperiodicity is probably due to the relatively broadtemperature tolerance of spruce (Piceaspp.), whichcomprises over 94% of forest biomass. Spruce is
relatively insensitive to growing season temperaturevariation (250-1990 degree days) and to wintertemperature minima (Pastor and Post 1985), whichreduced the effects of sequential cold winters or hotsummers in the treatment simulations. Aspen(Populus tremuloides) biomass did decrease during
PRECIPITATION CYCLES TEMPERATURE CYCLESCONTROL CONTROL
11 YR 4 Y R19 YR 11 YR
80 YR180 YR
Fig. 4. Spectral density of simulated biomass for four eco-systems in response to various climatic functions. Precipitationsimulations (left side) were control, 11 year cycle and 19 year cy-cle; temperature simulations (right side) were control, 4 year, 11year, 80 year and 180 year cycles. Simulated ecosystems, fromtop to bottom, are (a, e) shortgrass prairie, (b, f) boreal forest,(c, g) boreal/northern hardwoods transition forest, and (d, h)eastern hardwoods. Note that spectral density scale differsamong ecosystems.
some sequential cold periods, but it was a minorcomponent of total biomass. Drought events forthe boreal forest rarely occurred under any scenarioand were not a factor.
Response of the hardwood/boreal transitionforest (NE Minn) to low-frequency, high-amplitudetemperature fluctuations (80 and 180 year periods)occurred in two predominant phases (Fig. 3c). Athigh temperatures occurring in the early part of thecycle, sugar maple (Acer saccharuni) and yellowbirch (Betula alleghaniensis), both representative offorests south of the transition zone, increased in
biomass. Later in the cycle, as temperature de-creased, white spruce (Picea glauca) biomass in-creased while sugar maple and yellow birch biomassdecreased. The net result was a bimodal spectraldensity plot with a major peak corresponding to thedynamics of warm-weather species and a minorpeak corresponding to dominance by the cold-adapted white spruce (Fig. 4g). Under the high-frequency temperature cycles and the precipitationperiodicities, the spectral density peaks in the tran-sition forest were attenuated relative to the controlrun. The most probable reason for this attenuationis that the shorter cycles of smaller magnitude de-synchronized mortality of the dominant tree amongthe 30 replications. In the control run, the domi-nant species was sugar maple, with about 50% ofthe aboveground standing biomass. The maximumage of sugar maple in LINKAGES is 300 years, andthe peak in spectral density occurred at about 350years (Fig. 4c, g). Thus, after a tree-fall event in thecontrol run, a large amount of biomass would belost, and a replacement maple tree would not reachcanopy height and die again for another 300 years.Introduction of the high-frequency temperature cy-cles and the precipitation experiments improvedgrowing conditions, allowing growth spurts whichwere spread out in time relative to the control run;as a result, biomass did not show as strong a cy-clic response. Another contributing factor is themethod LINKAGES uses to calculate mortality intrees. When there were two consecutive years of lowgrowth, probability of mortality increased to 0.34for a tree. In the high-frequency cycles for bothprecipitation and temperature, the number of yearswith consecutive poor growth was not enough to in-crease species-specific mortality sufficiently to in-duce biomass cycles as occurred in the low-fre-quency cycles, yet it was sufficient to decouple the30 replications in time so that there was not a con-sistent cycle in biomass for the dominant tree spe-cies (sugar maple).
Eastern hardwood forest response to tempera-ture periodicity was striking for the low-frequency,high-amplitude scenarios (Fig. 4h). Eastern hard-wood dominants, i.e. tulip poplar (Liriodendrontulipifera), hickory (Caryaspp.) and oak (Quercusspp.) species showed drought stress responses to
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temperature shifts, with higher temperature phasesof the low-frequency cycle more than tripling theaverage number of growing season drought daysin comparison to lower temperature phases ofthe long-term cycle. Overall biomass decreasedmarkedly during such periods of increased droughtstress. As with the transition forest, attenuationwas also seen for the eastern hardwood forest underthe higher temperature cycle scenarios. In contrastwith the transition forest, however, spectral peakswere never bimodal, indicating that all dominantspecies in this forest system responded similarly tostresses introduced by an oscillating climate.
The two ecosystems that were relatively insensi-tive to climatic periodicities, the shortgrass prairieand the boreal forest, were each dominated by aspecies with broad climatic tolerances. Grasslands,moreover, have much less internally-structured cy-cling. The higher spectral power estimates andwhite noise test statistics for forest systems underrandom climatic variation indicates that the forestsmodeled here possess much stronger internal fre-quencies than the shortgrass prairie. This resultsfrom the way regeneration and mortality are treat-ed. Trees in the forest systems are modeled with in-creasing probability of death as they approach aspecies-specific expected longevity, with the proba-bility of mortality in mature trees increasing greatlyduring stressful periods where water or light be-comes limiting, particularly when stress conditionsoccur in two consecutive years. Average lifespansfor dominant tree species in the system (roughly150-400 years) are therefore likely to be coupled topredicted periodicities in biomass. By contrast,Bouteloua gracilis is not assigned a maximum age.The major factor expected to influence periodicityin STEPPE is the probability of seed production,which is a function of annual precipitation.
Internal frequencies of an ecosystem associatedwith plant demographics can be modified by exter-nal periodicities in climate, particularly when theexternal signal becomes synchronized with the in-ternal signal. Responses occurred in hardwoodforests as larger-amplitude, lower-frequency tem-perature oscillations crossed biological thresholdsfor dominant species. Serial correlations in temper-ature caused significant differences in biomass
response in the boreal hardwood transition zone us-ing LINKAGES (Cohen and Pastor 1991). The na-ture of model response is a function of the charac-teristics of the dominant species (Coffin and Urban1993). We have extended the results of those studiesacross a broad geographic and climatic range inNorth America. The climate periodicities we usedwere derived from long-term climate data series attimescales sufficient to capture low frequency dy-namics in these models (Emanuel et al. 1978; Jassbyand Powell 1990). These periodicities sometimesresulted in fundamentally different model re-sponses when compared with simulations using thetraditional approach of stochastic variation abouta long-term mean. Further, at a biome transition,we found that both amplification and attenuationeffects resulted from climatic oscillations, in accor-dance with Gosz and Sharpe (1989).
Our results showing significant differences be-tween the standard input methodology and the cy-clic input structures for hardwood forest biomassimply that the way ecosystem modelers simulate cli-mate input should be carefully considered. Werecommend that preliminary sensitivity analyses beconducted in the frequency domain as a standardscreening step (e.g., Dwyer and Kremer 1983). Ifclimate is known to have significant multi-annualperiodicity(s) and if the system being simulated hasstrong internal frequencies that can be amplified orattenuated by the input signal, predictions of long-term biomass response and system behavior willdiffer significantly from predictions using randomclimate input. This disparity could be particularlylarge when modeling vegetation at biome transi-tions.
Acknowledgements
This work originated as an inter-university gradu-ate student project at the Clowes Ecosystem Model-ing Workshop, November, 1990, organized byJerry Melillo and Ed Rastetter at the EcosystemCenter, Marine Biological Laboratory, WoodsHole, Massachusetts. In addition, we acknowledgeBill Lauenroth, John Pastor and Hank Shugart forsupport, consultation and patience in allowing us to
259
conduct this work concurrently with our respectivedissertation efforts. We further acknowledge help-ful comments from Debra Coffin, Yosef Cohen,Bruce Hayden, Tom Kirchner, Robert Scheller,Dean Urban and two anonymous reviewers. Partialfunding support for the authors during this projectwas provided by the Coweeta LTER, Los AlamosNational Environmental Research Park, NASA,NSF-BSR, and USDA-Forest Service.
References
Agren, G.I., McMurtrie, R.E., Parton, W.J., Pastor, J.P. andShugart, H.H. 1991. State-of-the-art of models of pro-duction-decomposition linkages in conifer and grasslandecosystems. Ecol. Applic. 1: 118-138.
Allen, T.H.F., O'Neill, R.V. and Hoekstra, T.W. 1984. Inter-level Relations in Ecological Research and Management:Some Working Principles from Hierarchy Theory. GeneralTechnical Report RM-110. Fort Collins, CO: USDA-RockyMountian Forest and Range Experimental Station.
Bonan, G.B. and Sirois, L. 1992. Air temperature, tree growth,and the northern and southern range limits to Picea mariana.J. Veg. Sci. 3: 495-506.
Botkin, D.B., Janak, J.F. and Wallis, J.R. 1972. Some ecologi-cal consequences of a computer model of forest growth. J.Ecol. 60: 849-872.
Broecker, W.S. 1975. Climatic change: are we on the brink ofa pronounced global warming? Science 189: 460-463.
Brown, R.G. 1983. Introduction to Random Signal Analysis andKalman Filtering. John Wiley & Sons, New York.
Burke, I.C., Kittel, T.G.F., Lauenroth, W.K., Snook, P. andYonker, C.M. 1991. Regional analysis of the central GreatPlains: sensitivity to climate variability. BioSci. 41: 685-692.
Burroughs, W.J. 1992. Weather Cycles: Real or Imaginary?Cambridge University Press, Cambridge.
Cale, W.G., Henebry, G.M. and Yeakley, J.A. 1989. Inferringprocess from pattern in natural communities. BioSci. 39:600-605.
Coffin, D.P. and Lauenroth, W.K. 1990. A gap dynamics simu-lation model of succession in a semiarid grassland. Ecol.Mod. 49: 229-266.
Coffin, D.P. and Lauenroth, W.K. 1991. Effects of competitionon spatial distribution of roots of blue grama. J. RangeMgmt. 44: 68-71.
Coffin, D.P. and Urban, D.L. 1993. Implications of natural his-tory traits to system-level dynamics: comparisons of a grass-land and a forest. Ecol. Mod. 67: 147-178.
Cohen, Y. and Pastor, J.P. 1991. The responses of a forestmodel to serial correlations of global warming. Ecol. 72:1161-1165.
Currie, R.G. and O'Brien, D.P. 1988. Periodic 18.6-year and
cyclic 10 to 11 year signals in Northeastern United Statesprecipitation data. J. Clim. 8: 255-281.
Currie, R.G. and O'Brien, D.P. 1990. Deterministic signals inprecipitation in the Northwestern United States. WaterResour. Res. 26: 1649-1656.
Davis, M.B. and Botkin, D.B. 1985. Sensitivity of cool-temperate forests and their fossil pollen record to rapid tem-perature change. Quat. Res. 23: 237-240.
DeAngelis, D.L. and Waterhouse, D.C. 1987. Equilibrium andnonequilibrium concepts in ecological models. Ecol. Monog.57: 1-21.
DeAngelis, D.L., Post, W.M. and Travis, C.C. 1986. PositiveFeedback in Natural Systems. Springer-Verlag, N.Y.
Dwyer, R.L. and Kremer, J.N. 1983. Frequency-domain sensi-tivity analyses of an estuarine ecosystem simulation model.Ecol. Mod. 18: 35-54.
Emanuel, W.R., West, D.C. and Shugart, H.H. 1978. Spectralanalysis of forest model time series. Ecol. Mod. 4: 313-326.
Enfield, D.B. 1989. El Nino, past and present. Rev. Geophys.27: 159-187.
Friend, A.D., Shugart, H.H. and Running, S.L. 1993. Aphysiology-based gap model of forest dynamics. Ecol. 74:792-797.
Fuller, W.A. 1976. Introduction to Statistical Time Series. JohnWiley & Sons, N.Y.
Gosz, J.R. and Sharpe, P.J.H. 1989. Broad-scale concepts forinteractions of climate, topography, and biota at biome tran-sitions. Land. Ecol. 3: 229-243.
Holdsworth, G., Krouse, H.R. and Nosal, M. 1992. Ice core cli-mate signals from Mount Logan, Yukon, A.D. 1700-1897.In Climate Since A.D. 1500. pp. 483-504. Edited by R.S.Bradley and P.D. Jones. Routledge, London.
Jassby, A.D. and Powell, T.M. 1990. Detecting changes in eco-logical time series. Ecol. 71: 2044-2052.
Jones, P.D., Wigley, T.M.L. and Wright, P.B. 1986. Globaltemperature variations between 1861 and 1984. Nature 322:430-434.
Kelly, P.M. and Wigley, T.M.L. 1992. Solar cycle length, green-house forcing and global climate. Nature 360: 328—330.
Kerr, R.A. 1984. Moon influences western U.S. drought.Science 224: 587.
Kienast, F. 1991. Simulated effects of increasing atmosphericCO2 and changing climate on the successional characteristicsof Alpine forest ecosystems. Land. Ecol. 5: 225-238.
Lauenroth, W.K., Urban, D.L., Coffin, D.P., Parton, W.J.,Shugart, H.H., Kirchner, T.B. and Smith, T.M. 1993.Modeling vegetation structure-ecosystem process interactionsacross sites and biomes. Ecol. Mod. 67: 49-80.
Lean, J. and Rind, D. 1994. Solar variability: implications forglobal change. Eos. Trans. AGU 75: 1, 5-7.
Michaels, P.J. and Hayden, B.P. 1987. Modeling the climatedynamics of tree death. BioSci. 37: 603-610.
Mitchell, J.M. 1976. An overview of climatic variability and itscausal mechanisms. Quat. Res. 6: 481-493.
Neilson, R.P., King, G.A. and Koerper, G. 1992. Toward a rule-based biome model. Land. Ecol. 7: 27-43.
O'Neill, R.V., DeAngelis, D.L., Waide, J.B. and Allen, T.H.F.1986. A Hierarchical Concept of Ecosystems. PrincetonUniversity Press, Princeton, New Jersey.
O'Neill, R.V., Johnson, A.R. and King, A.W. 1989. A hierar-chical framework for the analysis of scale. Land. Ecol. 4:193-205.
Overpeck, J.T., Rind, D. and Goldberg, R. 1990. Climate-induced changes in forest disturbance and vegetation. Nature343: 51-53.
Pastor, J.P. and Post, W.M. 1985. Development of a LinkedForest Productivity-Soil Process Model. ORNL/TM-9519Oak Ridge National Laboratory, Oak Ridge, Tennessee,USA.
Pastor, J.P. and Post, W.M. 1986. Influence of climate, soilmoisture, and succession on forest carbon and nitrogen cy-cles. Biogeochem. 2: 3-27.
Pastor, J.P. and Post, W.M. 1988. Response of northern forestto CO2 induced climate change. Nature 334: 55-58.
Platt, T. and Denman, K.L. 1975. Spectral analysis in ecology.Ann. Rev. Ecol. Syst. 6: 189-210.
Quinn, W.H. and Neal, V.T. 1992. The historical record ofEl Nino events. In Climate Since A.D. 1500. pp. 623-648.Edited by R.S. Bradley and P.O. Jones. Routledge, Lon-don.
Rastetter, E.B., Ryan, M.G., Shaver, G.R., Melillo, J.M.,Nadelhoffer, K.J., Hobbie, J.E. and Aber, J.D. 1991. Ageneral biogeochemical model describing the responses of theC and N cycles in terrestrial ecosystems to changes in CO2,climate and N deposition. Tree Physiol. 9: 101-126.
Rind, D. and Overpeck, J. 1994. Hypothesized causes ofdecadal-to-century climate variability: Climate model results.Quat. Sci. Rev. in press.
Ropelewski, C.F. and Halpert, M.S. 1986. North Americanprecipitation and temperature patterns associated with the ElNino/Southern Oscillation (ENSO). Mon. Weather Rev. 114:2352-2362.
Running, S.W. and Coughlan, J.C. 1988. A general model offorest ecosystem processes for regional applications I. Hydro-logical balance, canopy gas exchange and primary productionprocesses. Ecol. Mod. 42: 125-154.
Sala, O.E. and Lauenroth, W.K. 1982. Small rainfall events: anecological role in semiarid regions. Oecologia (Berlin) 53:301-304.
Sala, O.E., Lauenroth, W.K. and Parton, W.J. 1992. Long-
term soil water dynamics in the shortgrass steppe. Ecol. 73:1175-1181.
SAS/ETS User's Guide. 1982. Edited by A.A. Ray. SAS Insti-tute, Gary, North Carolina.
Schlesinger, M.E. and Ramankutty, N. 1992. Implications forglobal warming of intercycle solar irradiance variations. Na-ture 360: 330-333.
Shugart, H.H. 1984. A Theory of Forest Dynamics. Springer-Verlag, New York.
Shugart, H.H. 1987. Dynamic ecosystem consequences of treebirth and death patterns. BioSci. 37: 596-602.
Shugart, H.H. and West, D.C. 1977. Development of an Ap-palachian deciduous forest succession model and its applica-tion to assessment of the impact of the chestnut blight. J. Env.Mgmt. 5: 161-170.
Shugart, H.H. and Urban, D.L. 1989. Factors affecting the rela-tive abundance of forest tree species. In Toward a More ExactEcology. Edited by P.J. Grubb and J.B. Whittaker. Black-well Scientific Publications, Oxford.
Shugart, H.H., Emanuel, W.R., West, D.C. and DeAngelis,D.L. 1980. Environmental gradients in a simulation model ofa beech-yellow-poplar stand. Math. BioSci. 50: 163-170.
Smith, T.M. and Urban, D.L. 1988. Scale and resolution offorest structural pattern. Vegetatio 74: 143-150.
Stocker, T.F. and Mysak, L.A. 1992. Climatic fluctuations onthe century time scale: a review of high-resolution proxy dataand possible mechanisms. Clim. Change 20: 227-250.
Vines, R.G. 1982. Rainfall patterns in the western United States.J. Geophys. Res. 87: 7303-7311.
Weinstein, D.A. 1992. Use of simulation models to evaluate thealteration of ecotones by global carbon dioxide increases. InLandscape Boundaries: Consequences for Biotic Diversityand Ecological Flows, pp. 379-393. Edited by A.J. Hansonand F. di Castri. Springer-Verlag, New York.
Wigley, T.M.L. and Raper, S.C.B. 1990. Natural variability ofthe climate system and detection of the greenhouse effect. Na-ture 344: 324-327.
Yeakley, J.A. and Cale, W.G. 1991. Organizational levels anal-ysis: a key to understanding processes in natural systems. J.Theor. Biol. 149: 203-216.
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