Are ecosystem carbon inputs and outputs coupled at short time scales? A case study from adjacent pine and hardwood forests using impulse–response analysis


P. C. Stoy. Fax: +44 0131 662 0478; e-mail:


A number of recent studies have attributed a large proportion of soil respiration (Rsoil) to recently photoassimilated carbon (C). Time lags (τPR) associated with these pulses of photosynthesis and responses of Rsoil have been found on time scales of hours to weeks for different ecosystems, but most studies find evidence for τPR on the order of 1–5 d. We showed that such time scales are commensurate with CO2 diffusion time scales from the roots to the soil surface, and may thus be independent from photosynthetic pulses. To further quantify the role of physical (i.e. edaphic) and biological (i.e. vegetative) controls on such lags, we investigated τPR at adjacent planted pine (PP) and hardwood (HW) forest ecosystems over six and four measurement years, respectively, using both autocorrelation analysis on automated soil surface flux measurements and their lagged cross-correlations with drivers for and surrogates of photosynthesis. Evidence for τPR on the order of 1–3 d was identified in both ecosystems and using both analyses, but this lag could not be attributed to recently photoassimilated C because the same analysis yielded comparable lags at HW during leaf-off periods. Future efforts to model ecosystem C inputs and outputs in a pulse–response framework must combine measurements of transport in the physical and biological components of terrestrial ecosystems.


Soil respiration (Rsoil) is the largest terrestrial source of CO2 to the atmosphere and currently represents an annual flux an order of magnitude larger than that from anthropogenic fossil fuel emissions (Schimel 1995; Schlesinger 1997). Quantifying the processes that control the dynamics of Rsoil is thus critical to understanding the global carbon (C) cycle and the climate system. Despite its importance, there is a general lack of agreement on how Rsoil responds to environmental drivers and photosynthetic C inputs across short and long time scales (Reichstein et al. 2005a,b; Davidson & Janssens 2006). These difficulties arise from the multifactorial nature of the processes that control the magnitude and variability of Rsoil, and the affiliated time lags between environmental drivers and ecosystem responses (Table 1).

Table 1.  A summary of studies that investigated the relationship between aboveground processes and soil respiration (Rsoil) or ecosystem respiration (Reco) in forest and savanna ecosystems using non-destructive methods. PP and HW refer to the planted pine and hardwood forests in the Duke Forest, NC, respectively
StudyLag (d)MethodEcosystem
  • a

    Tang et al. (2005) also found evidence for a 7−12 h time lag between photosynthesis and Rsoil.

  • b

    Honeydew at tree base.

  • c

    For leaf, plant and ecosystem respiration.

  • PP, planted pine; HW, hardwood; EC, eddy covariance; W US, western United States; FACE, free-air carbon dioxide enrichment.

Horwath, Pretziger & Paul (1994)2–314CPopulus eumericana
Mikan et al. (2000)Multiple14CP. eumericana
Tang et al. (2005)5–6aEC/flux gradientQuercus douglasii savanna
Baldocchi et al. (2006)MultipleEC/flux gradientQ. douglasii savanna
Ekblad & Hogberg (2001)1–4δ13CBoreal mixed coniferous
Bowling et al. (2002)5–10δ13C6 W US coniferous forests
Barbour et al. (2005)3bδ13CNothofagus solandri
Knohl et al. (2005)4–5δ13CMixed deciduous
Mortazavi et al. (2005)3–4cδ13CPP and HW
Andrews et al. (1999)< 7δ13CPP/FACE experiment

In boreal and temperate ecosystems, Rsoil is thought to be determined primarily by soil temperature (Tsoil, see Appendix Table A1 for a list of abbreviations) (Lloyd & Taylor 1994). Soil moisture (θ) often plays an important role at the dry and wet ends of its distribution (Davidson, Belk & Boone 1998; Mielnick & Dugas 2000; Palmroth et al. 2005). In addition to the well-studied effects of Tsoil and θ, a number of recent studies have investigated the role of photosynthesis in determining the magnitude and variability of Rsoil after some time lag (τPR), suggesting that within-ecosystem carbon transport may be critical for understanding the biosphere–atmosphere exchange of C (Högberg et al. 2001; Ryan & Law 2005).

If models of Rsoil are to incorporate photosynthetic inputs of C (Högberg et al. 2001), it is necessary to understand how these two fluxes are coupled. The τPR reflects the sum of the time scales of C transport in the biological (τB) and soil (or physical, τP) components of the ecosystem (Fig. 1). The former includes the time required for C to travel from leaf to phloem to root or endomycorrhizal surface; respiration from these sources is often considered to be the ‘autotrophic’ component of Rsoil. The latter consists of CO2 diffusion in the soil air space after production from either autotrophic or heterotrophic sources. Studies employing stable isotope, radioisotope or automated ecosystem flux measurements in forested or savanna ecosystems generally find evidence for τ between photosynthesis and Rsoil or ecosystem respiration (Reco) on the order of hours (Tang, Baldocchi & Xu 2005), to days (Table 1) or even weeks (Mikan et al. 2000; Baldocchi, Tang & Xu 2006). However, no study to our knowledge has quantified the different roles of τB and τP in determining τPR.

Figure 1.

Top: A conceptual diagram of CO2 entry (via photosynthesis, P) and exit (via soil respiration, Rsoil) in a forested ecosystem. Time lags due to transport (τ) in the biological (τB) and physical (τP) components of the ecosystem are shown. The τP is purposely shown as tortuous. The general location of the eddy covariance (EC) and automated CO2 efflux systems (ACES) in this experiment is presented. The rooting depth and most respiratory activity in the study ecosystems are constrained by a clay pan at ca 30 cm as indicated. Bottom: Hypothetical time series of photosynthesis P(t) and soil respiration Rsoil(t) are shown for illustration. The impulse–response analysis attempts to determine the lag time between an impulse in photosynthesis, defined as an anomalous excursion from the diurnal cycle, and its response in the soil respiration (defined here as an anomalous excursion from the background state set by the instantaneous soil temperature and soil moisture series) using the cross-correlation function. The time separation between anomalous excursions in the soil respiration can also be determined from an autocorrelation analysis.

We note that Rsoil comprises, on average, 70% of Reco across temperate forested ecosystems (Janssens et al. 2001), such that τ between photosynthesis and Reco may largely reflect τ between photosynthesis and Rsoil. Whereas the signal of photosynthesis has been shown to be present in Rsoil measurements (Table 1), it remains unclear how τP and τB interact to influence τPR because both can vary with edaphic conditions and vegetative function.

A first-order estimate of τP can be determined from dimensional analysis:


where ZR is the root-zone depth and dmol.diff is the molecular diffusivity of CO2 in the soil, which depends on its molecular diffusivity in free atmosphere (datm) and tortuosity (ξ). While tortuousity is difficult to measure in porous media dominated by macropores (Suwa et al. 2004), an estimate of ξ can still be obtained using the Millington–Quirk relationship:


where η is soil porosity. As a case study, consider a situation where soil temperature is 20 °C such that datm ∼ 0.14 cm2 s−1 and ZR is small (e.g. 0.3 m) in a silt loam with η = 0.54. Based on these parameters, the time scales of CO2 diffusion from the root zone may vary between 1.5 and 6.0 d or longer for typical seasonal soil moisture states (Fig. 2), thus overlapping with literature estimates that may be interpreted as τB or both τB and τP (Table 1).

Figure 2.

Estimated transport time of gas-phase soil CO2 (τP) for typical growing season (solid symbols) and non-growing season periods at the planted pine (PP) and hardwood (HW) forest ecosystems using mean seasonal soil moisture (θ) under unsaturated conditions. The τP for PP is denoted by triangles and HW by circles.

In addition to the likely similarities between the magnitudes of τP and τB, biological storage of C and phenological effects may complicate the estimation of τPR and its variability. For example, tree-girdling studies have found large and rapid decreases in the magnitude of Rsoil after girdling (Högberg et al. 2001; Subke et al. 2004), variable responses that depend on stand composition (Andersen et al. 2005), or weak signals (Edwards & Ross-Todd 1979; Binkley et al. 2006). The variability in these responses may reflect the role of plant-stored C (Binkley et al. 2006) and thus may vary seasonally. For example, Cisneros-Dozal, Trumbore & Hanson (2006) traced an industrial pulse of 14C through an oak-hickory forest, and found that root respiration was generated from stored non-structural carbohydrates before the growing season and by recent photoassimilates near the peak of the growing season. Other variables likely to influence the velocity and seasonality of τB include distance from assimilation site to respiring tissue, phloem temperature and sap viscosity, and C sink strength and size, and plant allocation (McDowell et al. 2004; Barbour et al. 2005).

Thus, the coupling between photosynthesis and Rsoil depends on τP and τB, both of which may vary because of the biological and physical properties of the ecosystem. Some of these variables can be controlled for by studying adjacent ecosystems with similar meteorological and edaphic characteristics, but with different phenology.

Here, we examine time lags between canopy level flux measurements and Rsoil for multiple years in planted pine (PP) and hardwood (HW) forest ecosystems in the Duke Forest, NC. Specifically, we investigate the coupling between photosynthesis and Rsoil at shorter (e.g. daily) time scales (Table 1) to determine the ‘pulse–response’ relationship that may exist between ecosystem C inputs and outputs using continuous non-invasive flux measurements (Fig. 1). The study ecosystems are adjacent with identical climate and similar soil type, rooting depth, annual Rsoil and bulk soil C (K. Johnsen, unpublished results), such that differences in observed ecosystem dynamics are attributable to vegetative activity (Stoy et al. 2006a,b). The strong role of Tsoil and θ in controlling Rsoil at the daily time step at PP and HW has been well established (Palmroth et al. 2005). The purpose of the present study is to investigate the additional role of aboveground processes via canopy photosynthesis on Rsoil by extending a recent methodology proposed by Baldocchi et al. (2006) that employed automated measurements of canopy level and soil fluxes.

The PP and HW study ecosystems may represent a best-case scenario for disentangling the roles of τB and τP in controlling the coupling between photosynthesis and Rsoil in forests. A clay pan at ca 30 cm (Oren et al. 1998) constrains the vertical root distribution at both ecosystems (Fig. 1), such that τP is likely to be small but similar at these two stands – at least in terms of the seasonal variation in τP due to seasonal variations in soil moisture. Canopy activity is strongly diminished at PP when air temperature is less than 10 °C (Schäfer et al. 2002), but remains otherwise active during winter. However, canopy activity is entirely absent at HW during winter when the canopy is without leaf. Such periods can be investigated as a control case. In addition, near-continuous eddy covariance (EC) photosynthesis estimates and Rsoil measurements from automated carbon efflux systems (ACES, Butnor et al. 2003) are available for 6 years at PP and 4 years at HW, making it possible to investigate several combinations of phenological situations and climatic conditions.

Briefly, EC measures the turbulent flux of CO2 (net ecosystem exchange, NEE), water vapour (evapotranspiration, ET) and momentum between the biosphere and atmosphere (Baldocchi et al. 2001). Near-continuous, defensible long-term EC-based estimates of canopy C uptake by photosynthesis and ecosystem C loss through respiration can be derived using a variety of ‘flux partitioning methods’, which have been validated against independent and model-based canopy photosynthesis and ecosystem respiration measurements for the study ecosystems by Stoy et al. (2006b). Estimates of photosynthesis can also be derived using water flux measurements by assuming that transpiration dominates ET in forested ecosystems (during leaf-on periods in the case of HW forests) and that canopy water loss is coupled to CO2 gain through stomatal function.


Site description

The study ecosystems lay adjacent on Enon silt loam, a low fertility Hapludalf typical of the Southeastern United States (SE US) Piedmont, with a transition to Iredell gravelly loam in parts of HW (Pataki & Oren 2003). PP was established in 1983 and is comprised primarily of Pinus taeda L. with some emergent Liquidambar styraciflua L. Canopy height was 19 m in 2005. HW is an 80- to 100-year-old mixed deciduous forest dominated by oak (Quercus) and hickory (Carya) species. Canopy height averaged 25 m with emergent treetops reaching over 35 m. The canopies of both ecosystems are characterized by a diverse understory, and thus a large vertical distribution of leaf area (Stoy et al. 2005).

Rsoil measurements

Rsoil was measured using two ACES (US patent 6 692 970) developed by the United States Department of Agriculture (USDA) Forest Service (Butnor et al. 2003). The ACES coupled an infrared gas analyser (IRGA, EGM-3; PP Systems, Amesbury, MA, USA) with a chamber-based multi-port design to iteratively measure CO2 efflux from either stem or soil. ACES Rsoil measurements were easily corrected to give a consistent response for different soil types, and the system has been lab-calibrated against known CO2 efflux rates (Butnor & Johnsen 2004; Butnor, Johnsen & Maier 2005). The chambers included a pressure equilibration port to ensure that chamber and atmospheric pressure differences do not compromise accurate flux measurements.

For each ACES, 15 measurement chambers and one reference chamber were sampled by the IRGA. Chambers were sampled for 9 min after a 1-min purge, such that individual chambers were sampled every 160 min (ca 2.7 h). For this study, Rsoil measurements were available from six chambers at PP and eight chambers at HW. The remaining chambers were used to measure stem respiration or Rsoil in fertilized plots and were not considered here. We were interested in examining the pulse–response relationship between photosynthesis and Rsoil, and thus used the average of Rsoil normalized between 0 and 1 for each chamber for each 2.7 h measurement interval in this analysis.

The ACES at PP was located in Plot 8 of the Duke FACE study some 400 m south-southwest (SSW) of the EC system located in Plot 1 (Palmroth et al. 2005; Stoy et al. 2006a). The portion of PP surrounding Plot 1 (i.e. within the EC flux footprint) had slightly lower C flux magnitude than the rest of the forest, such that the magnitude of measured NEE was some 50 g C m−2 y−1 lower than the plot as a whole (Oren et al. 2006). We assumed that, although the absolute quantities of Rsoil sampled by the ACES may not represent Rsoil of the EC measurement footprint at PP, the temporal pattern of Rsoil does not vary systematically at this uniformly planted stand. At HW, the ACES chambers were situated within 50 m of the EC measurement tower in an area commonly enveloped by the flux footprint.

ET and EC measurements

We note again that EC systems measure the biosphere/atmosphere flux of both water (i.e. ET) and CO2 (NEE), and that Rsoil is an important component of NEE. To avoid the inherent correlations that exist between two measurements that both capture soil CO2 efflux, we used estimates of ET rather than NEE as a surrogate for canopy photosynthesis when photosynthesis exists. The fundamental relationship between ecosystem C and H2O follows from considering the Fick's law relationship between canopy conductance (Gc) and gross ecosystem productivity (GEP), itself related to canopy photosynthesis (Goulden et al. 1997; Stoy et al. 2006b):


where ε is a conversion factor to account for differences in diffusivity between H2O and CO2 (1/1.6), and Ci/Ca is the ratio of leaf mesophyll to atmospheric (CO2), and is related to vapour pressure deficit (D) both at short and long time scales at PP and HW (Leuning 1995; Katul, Leuning & Oren 2003; Mortazavi et al. 2005). Gc dominates ET at the study ecosystems (Stoy et al. 2006a), and the relationship between ET and GEP is extremely strong; using monthly averages, P < 10−3 at both ecosystems with r2 = 0.83 and 0.95 at PP and HW, respectively (Fig. 3). ET is comprised entirely of evaporation (E) in the absence of Gc[i.e. during winter in the deciduous HW or when Gc is limited by airtemperatures of less than 10 °C at PP (Schäfer et al. 2002)]. Ecosystem E is dominated by E from the soil surface, which is primarily an energy-limited process when θ is high (Brutsaert 1982), as found during wintertime periods in both ecosystems (Stoy et al. 2006a). As an independent check, we also analysed time lags in the relationship between photosynthetically active radiation (PAR) and Rsoil. PAR was strongly related to GEP on hourly to daily time scales at both ecosystems (Stoy et al. 2005).

Figure 3.

The relationship between measured evapotranspiration (ET) and estimated gross ecosystem productivity (GEP) at the planted pine (PP, closed triangles) and hardwood (HW, open circles) forest study ecosystems at the monthly time scale.

ET was measured using EC systems comprised of triaxial sonic anemometers (CSAT3; Campbell Scientific, Logan, UT, USA) and open-path infrared gas analysers (IRGA, LI-7500; Li-Cor, Lincoln, NE, USA) positioned at 20.2 m at PP and at 39.8 m at HW. A closed-path gas analyser (LI-6262; Li-Cor) was employed at PP before 1 May 2001 (Katul et al. 1997b). The Webb–Pearman–Leuning correction (Webb, Pearman & Leuning 1980) for the effects of air density fluctuations on flux measurements was applied to scalar fluxes measured with the open-path LI-7500 (Li-Cor). More information on measurement details and data quality assurance can be found elsewhere (Katul et al. 1997a; Detto & Katul 2007; Stoy et al. 2006a,b).

Data analysis

We seek to examine the lag relationship between photosynthetic C assimilation and Rsoil. For this analysis, it is necessary to estimate both τB and τP. We did so by performing two analyses that differ in their underlying assumptions and data inputs:

  • 1Memory analysis on measured Rsoil. The basic assumption in the memory analysis is that internal autocorrelation in the Rsoil time series on short time scales is due to autocorrelation in the physical drivers of Rsoil and variations in carbon input. Hence, by removing the effects of the physical drivers (and their memory) on Rsoil, the memory in the residual series may reflect the memory injected by the carbon input (which is zero for the HW during winter, but finite for summer runs at both ecosystems). Algorithmically, an autocorrelation analysis on Rsoil for every week of the measurement period was used to determine the time lags at which the time series is no longer autocorrelated. Significant correlation (abbreviated σ) was determined using the classic approach of Anderson (1942) as described in Salas et al. (1988) and demonstrated in more detail in Appendix B. We then estimated τB by examining autocorrelation in the residual Rsoil time series (Rres) after removing the effects of soil transport due to diffusion and heterotrophic respiration due to soil temperature using
  • where f(τP) = ξ−1, to represent the dominant effects of tortuosity (and hence soil moisture) in controlling the variability of soil CO2 diffusion (Fig. 2). Palmroth et al. (2005) found that the Q10 function describes the temperature response of Rsoil better than alternate formulations after Lloyd & Taylor (1994) or Arrhenius (1889) at the study ecosystems. Rres reflects the time separation in anomalous events, taken here to mean events not explained by soil temperature and soil moisture, and as an indicator of τB It is important to note that both autotrophic and heterotrophic respiration is likely to respond to both Tsoil and θ, possibly in a similar manner. However, to conservatively identify any pulse–response events due to τB, we removed the effects of Tsoil and θ from Rsoil after Eqn 4 for the purpose of the residual analysis.

  • 2A cross-correlation analysis between ET or PAR and Rsoil or Rres. In essence, this cross-correlation analysis is conceptually analogous to the analysis reported in Tang et al. (2005) & Baldocchi et al. (2006). We computed (σ) for time lags of up to 6 d using a 10 d moving window. This analysis ensured that at least 30 data points were included in the computation of σ, noting that if all ACES chambers were averaged, then nine measurements were available daily. We note that a correlation analysis of periodic time series inherently induces both positive and negative correlation (e.g. Appendix Fig. B1c); we are interested in those cases when an increase or decrease in aboveground activity induces an affiliated increase or decrease in belowground activity, respectively.

All time series showed evidence of diurnal variability, and the auto- or cross-correlations of time series that share diurnal variations may be ‘contaminated’ by the diurnal cycle. We removed the diurnal trend of (i.e. ‘detrended’) the Tsoil, ET and PAR time series using a Fourier transformation/Lorentz thresholding methodology (Katul & Vidakovic 1998; Wesson, Katul & Siqueira 2003) described in more detail in Appendix B.

Rsoil is strongly controlled by Tsoil at the study ecosystems (Palmroth et al. 2005); therefore significant autocorrelation in the Tsoil signal or cross-correlation between Tsoil and aboveground surrogates for photosynthesis may result in artifactual σ. We removed from the analysis all time periods for which significant autocorrelation or cross-correlation with detrended Tsoil was present. Despite the strict requirements for data acceptability, the length of the data record ensured that a wide variety of environmental and phenological conditions were sampled. We separated the analysis into summer (May–August) and winter (November–February) to investigate the periods where canopy photosynthesis is absent at HW.


Ecological measurements

To motivate the analysis of σ between Rsoil, edaphic, and aboveground driving variables, we first described the features of the data record. The Rsoil, Tsoil, θ and ET time series for the 2000–2004 time period have been described elsewhere (Palmroth et al. 2005; Stoy et al. 2006a; Katul et al. 2007); we reiterate some of the basic trends as a background for later interpretation. We then investigate autocorrelation in the Rsoil and Rres time series, as well as cross-correlations between both Rsoil and Rres and the surrogates of photosynthesis, ET and PAR.

At both ecosystems, Rsoil, Tsoil and ET increased and θ decreased during the growing seasons of the measurement period (Fig. 4). Maximum monthly Rsoil during the severe drought in 2002 was observed during a period of high Tsoil when ET was relatively low compared with similar periods during other growing seasons (Fig. 4a,b). PP is a drought-sensitive ecosystem, and reductions in Gc and, thereby, photosynthesis are observed when θ is less than 0.2 m3 m−3 (Oren et al. 1998; Stoy et al. 2005).

Figure 4.

The monthly average of soil respiration (Rsoil), soil temperature (Tsoil) and canopy conductance (Gc) at the planted pine [PP, (a)] and hardwood [HW, (b)] forest ecosystems. Time series were normalized to have a maximum of 1 and minimum of 0 for comparison. (c) Normalized soil moisture (θ) measurements at the PP and HW ecosystems.

Memory analysis

The 10 d Rsoil time series were autocorrelated at time scales of ca 1.5–3 d on average in the study ecosystems during both summer and winter (Fig. 5a). These are approximately the time scales associated with C transport from photosynthesis and Rsoil at the study ecosystems (Mortazavi et al. 2005) and other ecosystems (Table 1), but we note that a time lag of similar length is also present at HW in winter when photosynthetic inputs are absent (Fig. 5a).

Figure 5.

(a) The mean value at which 10 d Rsoil autocorrelation functions cross the positive correlation threshold of Anderson (1942). PP refers to the planted pine ecosystem, HW the hardwood forest, s to summer and w to winter. (b) Same as (a) but for Rsoil residual time series (Rres) obtained after removing the effects of physical turnover times after Eqn 3.

After removing the effects of Tsoil and ξ via Eqn 4, the mean Rsoil autocorrelation (i.e. Rres) drops to ca 0.7–1.5 d with strong variability that is not related to θ (P > 0.1) (Fig. 5b). The only significant difference between any two distributions of τ is between Rsoil and Rres for summertime periods at PP (two sample t-test, P < 0.05). As a whole, this analysis may suggest that τB is on the order of one day, but this value is shorter than estimated by previous studies (Andrews et al. 1999; Mortazavi et al. 2005). More importantly, autocorrelations at HW during winter are comparable with other periods at both ecosystems. Therefore, rather than representing biological autocorrelation, Rres seems to retain some memory from the physical system, likely due to the strong autocorrelation in the variable to which it responds most strongly, Tsoil. In short, the non-linear temperature response of Rsoil means that any mild residual memory in Tsoil can disproportionally impact the autocorrelation of the residual Rsoil. This analysis also demonstrates the sensitivity of the ‘memory’ in respiration to the detrended soil temperature memory, even after taking into account the relationship between Tsoil and Rsoil using Eqn 3.

The probability (p) of observing significant autocorrelation (σ) at some time lag, abbreviated p(στ), for the detrended Tsoil time series is unity at time lags of up to 1 d at PP and up to 3 h (i.e. 1 time step) at HW (Fig. 6). The p(στ) decreases rapidly at ca 2 d at both ecosystems, and is greater than the p(στ) of a random signal for all periods of up to 6 d. The strong memory in Tsoil (Fig. 6) at time scales of ca 2 d corresponds to the memory of the Rsoil and Rres time series (Fig. 6). It is clear from this analysis that τB may be difficult to estimate because of multiple and overlapping time scales that appear to be strongly affected by physical drivers, mainly the memory in soil temperature. Again, this memory in Tsoil is not surprising as a first-order estimate of thermal lags τthermal in the rooting zone may be determined by

Figure 6.

The probability (p) of observing a significant autocorrelation (σ) at lag time τ in detrended 10 d soil temperature (Tsoil) time series at the planted pine (PP) and hardwood (HW) forest ecosystems. Significant autocorrelation of a random time series would be expected 5% of the time as indicated by the dashed line.


where dmol.T is the molecular diffusivity of heat in the soil (roughly, dmol.T ≈ 250 cm2 d−1 for a clay soil at intermediate soil moisture) resulting in τthermal = 3.5 d. These results suggest that the conceptual anomalous excursions in the respiration time series of Fig. 1 are masked by τthermal and may not reflect anomalous excursions in photosynthesis but anomalous excursions in the soil heat flux.

Cross-correlation analysis

To independently assess these findings, we investigated next the correlations of both Rsoil and Rres with surrogates of photosynthesis as a check on the idea that internal system autocorrelation masks the relationship between ecosystem C inputs and outputs at short time scales at the study ecosystems.

The p(στ) for the cross-correlation of both Rsoil and Rres, and either detrended ET or detrended PAR (see Appendix B) was often greater than that of a random signal at time lags of up to 6 d (Fig. 7). We note that significant autocorrelation in the detrended Tsoil time series was nearly always evident at a time lag of 36 h or less (Fig. 6); therefore, p(στ) was computed for longer periods allowing us to focus on the possible effects of photosynthesis on Rsoil. Seasonal differences in p(στ) were evident at both ecosystems and are suggestive of a complex relationship between edaphic and aboveground drivers and Rsoil.

Figure 7.

The probability (p) of observing a significant correlation (σ) between soil respiration (Rsoil) and evapotranspiration (ET) or photosynthetically active radiation (PAR) at time lag τ at the planted pine [PP, (a)] and hardwood [HW, (b)] forest ecosystems during peak winter (w, November–February) and summer (s, May–August) periods. ETw, ETs, PARw and PARs are denoted by solid, dashed, dash-dot and dotted lines, respectively. Driving variables were detrended as discussed in the Appendix. Significant correlation between random time series would be expected 5% of the time as indicated by the dashed line. Approximate time scales of soil CO2 diffusion after Fig. 2 are indicated by the symbols. (c & d) Same as (a & b) but using Rsoil residuals (Rres) after Eqn 3.

The p(στ) at PP was between 0.05 and 0.15 for most time lags during both summer and winter for the relationship of both Rsoil (Fig. 7a) and Rres (Fig. 7c) with the surrogates for photosynthesis. During winter, p(στ) between surrogates for photosynthesis and both Rsoil and Rres tended to decrease at ca 3–4 d (indicated by the open triangle), which is similar to the estimated value of τP for typical winter θ (Fig. 2) when the soil is not saturated.

This result was also apparent at HW. The p(στ) between PAR and Rres decreased rapidly at a time lag of ca 5 d during non-growing season periods, similar to the τP during non-saturated mean wintertime soil conditions (Figs 2 & 7d). This response differed from p(στ) between surrogates of photosynthesis and Rsoil during summer, which has a peak at 4 d for the case of ET and 5.5 d for the case of PAR (Fig. 7b). Thus, it is clear that parts of the ‘physical’ signal are removed via Eqn 3, but it is difficult to fully remove τP from the time series as suggested by previous results (Figs 5 & 6). This complicates the estimation of τB. Again, we assume that there are no direct photosynthetic C inputs during winter at HW, and that ET is comprised entirely of E. These results demonstrate that the full effects of the physical system act on multiple time scales and are difficult to remove from the Rsoil time series at these two ecosystems. There are no clear peaks in p(στ) that correspond to an unambiguous relationship between photosynthesis and Rsoil, even after removing the physical effects of diffusion via equation 3 (i.e. Rres).

Combined results from both ecosystems suggest that aboveground inputs mediate existing time lags between Rsoil and physical drivers because p(στ) differs for summer and winter periods when canopy photosynthesis is absent at HW. Whereas a ‘signature’ of canopy inputs may be present in as much as the summer p(στ) may be different from that in winter (Fig. 7), it is difficult to deconvolve the time scales at which canopy processes interact with Rsoil. This is due in part to the long memory in the physical drivers that tend to mask any variations in C input.


Thus, whereas C outputs via Rsoil may be dominated by recent photosynthetic C inputs at both of our study sites (Andrews et al. 1999; Mortazavi et al. 2005; Taneva et al. 2006) and others (Table 1), understanding these dynamics based on a pulse–response time series framework may not be possible for ecosystems in which time scales of C transport in the physical and biological components of the ecosystem overlap. Independent estimates from other types of analyses (e.g. Table 1) remain essential for quantifying τB, and future studies should isolate potential lags between photosynthesis and C evolution at the root or endomycorrhizal surface. Likewise, measuring the simultaneous profiles of subsurface CO2 concentration, soil moisture and soil temperature at short time steps (say under 10 min) permits us to estimate directly the subsurface CO2 production profile (e.g. see formulations in Suwa et al. 2004) to better model τP. Thus, a measurement scheme that captures the time scales at which respiration and CO2 transport occur will provide the necessary temporal and spatial resolution to track the movement (and storage) of CO2 through the biological and physical components of the ecosystem using process-based CO2 production and transport models. Such models may take advantage of, for example, the simple formulations for tortuosity and soil respiration employed here. In addition, the cross-correlation analysis at various layers between CO2 production profiles and photosynthesis (or its surrogates) and forest floor fluxes should permit further constraints on τB. This method may prove to be promising because of recent advances in solid-state subsurface CO2 concentration measurements at unprecedented short time scales (e.g. Tang et al. 2005).


Support for this study was provided by the Department of Energy (DOE) through the FACE–forest-atmosphere carbon transfer and storage (FACTS) and Terrestrial Carbon Processes (TCP) programs, by the National Institute of Global Environmental Change (NIGEC) through the Southeast Regional Center at the University of Alabama, Tuscaloosa (DOE cooperative agreement DE-FC030-90ER61010) and by the South East Regional Center (SERC)–NIGEC Regional Climate Impact Analysis Program (RCIAP) Research Program. We would like to thank K. Wesson, C-T. Lai, Y. Parashkevov, H. McCarthy, H-S. Kim, A.C. Oishi, K. Schäfer, B. Poulter, E. Ward, J. Pippen, R. LaMorte, R. Nettles, K. Lewin, G. Hon, A. Mace and J. Nagy for logistical assistance in the Duke Forest.


Appendix A

A list of abbreviations can be found in Table A1.

Table A1.  A list of abbreviations with units and definitions
ACES Automated carbon efflux system
CippmLeaf internal CO2 concentration
CappmAtmospheric CO2 concentration
datmcm2 s−1Molecular diffusivity of CO2 in the free atmosphere
dmol.Tcm2 d−1Molecular diffusivity of heat in the soil
dmol.diffcm2 d−1Molecular diffusivity of soil CO2
DkPaVapour pressure deficit
EC Eddy covariance
ETmm time−1Evapotranspiration
FT Fourier transform
Gcmol m−2 s−1Canopy conductance to CO2
GEPg C m−2 s−1Gross ecosystem productivity
HW Hardwood forest ecosystem
NEEg C m−2 s−1Net ecosystem exchange of CO2
p (στ)FractionThe probability of observing significant autocorrelation at some time lag
PARµmol m−2 s−1Photosynthetically active radiation
PP Planted pine ecosystem
Q10 Temperature sensitivity of soil respiration
R10µmol m−2 s−1Base soil respiration at Tsoil = 10 °C
Recoµmol m−2 s−1Ecosystem respiration
Rsoilµmol m−2 s−1Soil respiration
Rresµmol m−2 s−1Residual soil respiration after removing the physical effects due to temperature and diffusion using equation 1
SE US Southeastern United States
Tsoil°CSoil temperature
ZRmRooting depth
ε Ratio of the binary molecular diffusivity of CO2/H2O
θm3 m−3Soil moisture
ηm3 m−3Soil porosity
ξ Tortuosity
σ Significant autocorrelation
τdTime lag
τBdTime lag in the biological (i.e. vegetative) components of the ecosystem
τPdTime lag in the physical components of the ecosystem
τPRdTime lag between photosynthesis and soil respiration
τthermaldThermal lag in the rooting zone

Appendix B

The time series of environmental drivers and Rsoil measurements showed strong diurnal variability (Palmroth et al. 2005; Stoy et al. 2006a) and any correlation analysis between such time series would result in significant relationships at regular intervals. To avoid this situation, we removed the diurnal signal from the 2.7 h data by computing the Fourier transform (FT) of the solar zenith angle time series and removing the dominant frequencies from the time series of the environmental drivers. The diurnal mode of variability may be partially described by more than one Fourier coefficient (Fig. B1a); we used a Lorenz thresholding approach (Katul & Vidakovic 1998; Wesson et al. 2003) to ensure full removal of the most energetic frequencies, that is, those that describe diurnal variability (Fig. B1a,b). The detrended time series were then reconstructed using the inverse FT, and cross-correlation analysis was performed. Significance was determined using the approach of Anderson (1942) (Fig. B1c).


Figure B1. (a) The Fourier transform (FT) of a 10 d solar zenith angle time series with a 2.7 h measurement interval. The Nyquist frequency is denoted by the dotted line. Coefficients that describe the energetic diurnal frequencies were removed using the Lorenz thresholding methodology demonstrated in panel (b); coefficients for which the slope of the energy loss curve was greater than 1 were removed and the detrended time series of flux and environmental drivers were reconstructed using the inverse FT. (c) An example of the cross-correlation analysis between canopy conductance (Gc) and soil respiration (Rsoil) from chamber 1 of the automated carbon efflux system (ACES) at the planted pine (PP) forest during a 10 d period in April 2000. Significance was determined using the 95% probability threshold (dashed line) described by Anderson (1942).