Ecosystems

, Volume 11, Issue 2, pp 250–269

Integration of Process-based Soil Respiration Models with Whole-Ecosystem CO2 Measurements

Authors

    • Department of MathematicsUniversity of Utah
    • Department of MathematicsAugsburg College
  • D. J. P. Moore
    • National Center for Atmospheric Research
    • Department of GeographyKing’s College London
  • W. J. Sacks
    • Center for Sustainability and the Global Environment, Nelson Institute for Environmental StudiesUniversity of Wisconsin-Madison
  • R. K. Monson
    • Department of Ecology and Evolutionary Biology (EEB)University of Colorado
  • D. R. Bowling
    • Department of BiologyUniversity of Utah
  • D. S. Schimel
    • National Center for Atmospheric Research
Article

DOI: 10.1007/s10021-007-9120-1

Cite this article as:
Zobitz, J.M., Moore, D.J.P., Sacks, W.J. et al. Ecosystems (2008) 11: 250. doi:10.1007/s10021-007-9120-1

Abstract

We integrated soil models with an established ecosystem process model (SIPNET, simplified photosynthesis and evapotranspiration model) to investigate the influence of soil processes on modelled values of soil CO2 fluxes (RSoil). Model parameters were determined from literature values and a data assimilation routine that used a 7-year record of the net ecosystem exchange of CO2 and environmental variables collected at a high-elevation subalpine forest (the Niwot Ridge AmeriFlux site). These soil models were subsequently evaluated in how they estimated the seasonal contribution of RSoil to total ecosystem respiration (TER) and the seasonal contribution of root respiration (RRoot) to RSoil. Additionally, these soil models were compared to data assimilation output of linear models of soil heterotrophic respiration. Explicit modelling of root dynamics led to better agreement with literature values of the contribution of RSoil to TER. Estimates of RSoil/TER when root dynamics were considered ranged from 0.3 to 0.6; without modelling root biomass dynamics these values were 0.1–0.3. Hence, we conclude that modelling of root biomass dynamics is critically important to model the RSoil/TER ratio correctly. When soil heterotrophic respiration was dependent on linear functions of temperature and moisture independent of soil carbon pool size, worse model-data fits were produced. Adding additional complexity to the soil pool marginally improved the model-data fit from the base model, but issues remained. The soil models were not successful in modelling RRoot/RSoil. This is partially attributable to estimated turnover parameters of soil carbon pools not agreeing with expected values from literature and being poorly constrained by the parameter estimation routine. We conclude that net ecosystem exchange of CO2 alone cannot constrain specific rhizospheric and microbial components of soil respiration. Reasons for this include inability of the data assimilation routine to constrain soil parameters using ecosystem CO2 flux measurements and not considering the effect of other resource limitations (for example, nitrogen) on the microbe biomass. Future data assimilation studies with these models should include ecosystem-scale measurements of RSoil in the parameter estimation routine and experimentally determine soil model parameters not constrained by the parameter estimation routine.

Keywords

model-data fusionnet ecosystem exchangeecosystem modelparameter estimationeddy covarianceheterotrophic respiration

Introduction

Soils are important in the terrestrial carbon cycle for their role in the cycling and storage of carbon (Jenkinson and Rayner 1977; Schimel and others 1994; Jobbagy and Jackson 2000; Trumbore 2000; Raich and others 2002). Soil processes such as decomposition are strongly influenced by soil microbial communities (Fierer and others 2003; Lipson and Schmidt 2004; Crawford and others 2005; Monson and others 2006b; Göttlicher and others 2006). These microbial communities have been found to be quite heterogenous exhibiting both temporal (Lipson and Schmidt 2004) and spatial variation (Fierer and others 2003) in species assemblage. Temperature and other environmental factors such as moisture strongly influence these microbial communities and their associated CO2 fluxes from soil (Davidson and Janssens 2006). Current projections of increased surface temperature and changes in moisture (Alley and others 2007) will likely affect soil microbial interactions, ultimately changing the efflux of CO2 from soils and producing feedbacks in the terrestrial carbon cycle (Schimel and Gulledge 1998).

From an ecosystem perspective, the CO2 produced from respiration by soil organisms and its subsequent diffusion from the soil is a large component in the overall net ecosystem CO2 exchange (NEE, a complete list of symbols used to refer to fluxes is given in Table 1) (Goulden and others 1996; Lavigne and others 1997; Janssens and others 2001; Griffis and others 2004; Davidson and others 2006b; Monson and others 2006a, b; Chapin and others 2006). Measurements of NEE can complement manipulative experiments and elucidate how biological processes contribute to terrestrial ecosystem CO2 exchange. For example, recent studies at a high-elevation subalpine forest (the Niwot Ridge AmeriFlux site) demonstrated that winter soil respiration (RSoil) contributes to 35–48% of total ecosystem respiration (TER), with a large proportion of this respiration from microbial biomass (Monson and others 2006a, b). Additionally, seasonal variation in observed soil respiration fluxes is coincident with seasonal variation in microbial community composition (Lipson and others 2000; Lipson and Schmidt 2004; Monson and others 2006b).
Table 1.

List of Abbreviations for Flux Variables Used in Text

Symbol

Units

Description

GEE

g C m−2 day−1

Gross primary production flux

TER

g C m−2 day−1

Total ecosystem respiration flux

RH

g C m−2 day−1

Soil heterotrophic respiration flux

RW

g C m−2 day−1

Wood respiration flux

RL

g C m−2 day−1

Leaf respiration flux

RFine-Root

g C m−2 day−1

Fine root respiration flux

RCoarse-Root

g C m−2 day−1

Coarse root respiration flux

RRoot

g C m−2 day−1

Root respiration flux (= RFine-Root + RCoarse-Root)

RGrowth

g C m−2 day−1

Microbe growth respiration flux

RSoil

g C m−2 day−1

Soil respiration flux (includes root and heterotrophic components)

RA

g C m−2 day−1

Autotrophic respiration flux (includes wood, leaf, and root components)

NEE

g C m−2 day−1

Net ecosystem exchange of CO2 (= GEE − TER)

NPP

g C m−2 day−1

Net primary production (= GEE − RA)

\(\overline{{\text{GEE}}}\)

g C m−2 day−1

Mean GEE over the last 5 days

\(\overline{{\text{NPP}}}\)

g C m−2 day−1

Mean NPP over the last 5 days

Long-term records of NEE are a good candidate to investigate how environmental variation affects soil fluxes. Plot-level experimentation has shown differential responses of autotrophic and heterotrophic respiration to environmental drivers such as temperature, moisture, and substrate supply (Tang and others 2005b; Borken and others 2006; Hartley and others 2006; Scott-Denton and others 2006). As NEE is an aggregate measurement of ecosystem processes, long-term records of NEE can potentially be used to independently determine autotrophic and heterotrophic ecosystem respiration.

Modelling is an approach well-suited to exploring how soil carbon processes affect NEE, as direct soil measurements can induce a disturbance to the soil matrix and potentially bias results (Ryan and Law 2005). Recent reviews of soil measurements and soil modelling have emphasized the need for greater focus on understanding the short-term controls of soil respiration and coupling of belowground processes with aboveground processes (for example, photosynthesis) (Smith and others 1998; Fitter and others 2005; Ryan and Law 2005; Trumbore 2006; Davidson and others 2006a).

Plot-level measurements of RSoil are part of the standard measurements at many FLUXNET sites (http://www.fluxnet.ornl.gov/fluxnet). At the Niwot Ridge AmeriFlux site, Scott-Denton and others (2003) showed that the rhizospheric component (roots plus nearby microbes) is a significant contributor to RSoil. A subsequent study showed that autotrophic (root) and heterotrophic (microbial) respiration responded differently to environmental variation (Scott-Denton and others 2006), as summertime decreases in RSoil resulted from lower heterotrophic, rather than autotrophic, contributions to RSoil. The SIPNET ecosystem model (simplified photosynthesis and evapotranspiration model) is a useful tool at FLUXNET sites to decompose NEE into its component fluxes of photosynthesis (GEE) and TER (Braswell and others 2005; Sacks and others 2006, 2007). The current version of SIPNET does not explicitly model the contribution of roots or microbes to RSoil.

Model-data fusion or data assimilation techniques to extract information from models and observations (Raupach and others 2005) is a strategy to understand soil processes by directly using long-term records of NEE. One application of model-data fusion in the environmental science community is to extract meaningful information about ecosystem processes (such as process-level parameters) from the inherent stochasticity in environmental observations (Braswell and others 2005; Clark 2005; Knorr and Kattge 2005; Raupach and others 2005; Williams and others 2005; Xu and others 2006; Sacks and others 2007). Model-data fusion can determine which parameters are well-constrained by the existing data. Identifying the poorly constrained parameters thereby focuses future measurements on the processes in most need of further research. Comparing different models of soil respiration with the same data assimilation framework assists in model selection and makes identification of poorly constrained parameters and processes more robust.

The objective of this study was to model at the ecosystem level the rhizospheric and heterotrophic contributions of RSoil with SIPNET. To constrain the model, we used a multi-year dataset that consists of net CO2 fluxes made at the Niwot Ridge AmeriFlux site in conjunction with a model-data fusion approach to estimate model parameters. Our results were evaluated by (a) model predictions of measured ecosystem fluxes, (b) comparisons of the modelled contributions of RSoil to TER, root respiration (RRoot) to RSoil, and (c) literature comparisons of these quantities and estimated parameters.

Materials and Methods

Site Description

Measurements for this study were made at the Niwot Ridge AmeriFlux site, a subalpine forest at 3050 m elevation west of Boulder, Colorado (40°1’58”N; 105°32’46”W). The three dominant conifer species at Niwot Ridge include subalpine fir (Abies lasiocarpa), Engelmann spruce (Picea engelmannii), and lodgepole pine (Pinus contorta). Mean annual precipitation averages 800 mm and the mean annual temperature is 1.5°C (Monson and others 2002). The site has been extensively studied; for further details, see Bowling and others (2001, 2005), Monson and others (2002, 2006a, b), Scott-Denton and others (2003, 2006), Turnipseed and others (2003, 2004), Yi and others (2005), and Sacks and others (2007).

Net ecosystem exchange (NEE) was measured via eddy covariance. Details about the eddy covariance and meteorological measurements at Niwot Ridge can be found in Monson and others (2002). From November 1998 through the present, half-hourly fluxes of CO2 along with corresponding climate data have been measured at this site. For this study, we used half-hourly flux and meteorological data from 1 November 1998 to 31 December 2005 aggregated into a twice-daily timestep. A net CO2 flux measurement determines NEE, which is equal to the sum of photosynthesis (GEE) and total ecosystem respiration (TER). Sign conventions in the micrometeorological literature (and here) typically define all nonradiative CO2 fluxes as positive when directed to the atmosphere, so the GEE flux is negative and the TER flux is positive. Gaps in the half-hourly flux data arose from instrument malfunction or periods of atmospheric stability which can underestimate the flux measurement. These half-hourly gaps were then filled with nonlinear regression or functional fits with environmental variables such as incoming radiation, air temperature, or soil temperature (Monson and others 2002). If more than 50% of the half-hourly flux data for a given twice-daily timestep was gap-filled, this timestep was excluded from the data assimilation routine. Sacks and others (2006) further described the gap-filling and data processing methods used.

The Niwot Ridge forest is aggrading carbon, with cumulative annual NEE ranging from −60 to −80 g C m−2 (Monson and others 2002). These values for cumulative NEE are lower than other forest ecosystems and are attributable to the fact that this is a high-elevation site with extreme climate conditions (Monson and others 2002).

In addition to NEE, six additional climate variables measured at the site were used in the model: air temperature, soil temperature, precipitation, flux density of photosynthetically active radiation, relative humidity, and wind speed. The model was run on a twice-daily time step. The exact length of each day or night time step was determined from the day of year and latitude. For this study CO2 fluxes are reported as g C m−2 day−1.

SIPNET Ecosystem Model

The basic model formulation of SIPNET has been described in previous papers (Braswell and others 2005; Sacks and others 2006, 2007). SIPNET is a simplified version of the PnET family of models (Aber and Federer 1992; Aber and others 1996). The base model for SIPNET has three vegetation carbon pools (wood, leaves, and soil) and includes a model for soil moisture. The soil moisture model was developed by Sacks and others (2006) and is described in detail in that study. The initial conditions and fluxes are characterized by parameters listed in Table 2. Because Niwot Ridge is a coniferous forest, the model assumes an evergreen phenology. Biomass is added at a rate proportional to the net primary productivity (photosynthesis less autotrophic respiration, NPP). Photosynthesis adds biomass to the wood carbon pool and is the only way that carbon can be added to the ecosystem. Allocation to other carbon pools (such as leaves) decreases the wood carbon pool.
Table 2.

SIPNET Parameters and Initial Conditions

Parameter

Description

Model

Range/value

Source

Base

Roots

Quality

Initial pool values

CW,0

Initial wood carbon content (g C m−2)

9600

RM

CL,0

Initial leaf area index (m2 m−2)

4.2

M02

CS,0

Initial soil carbon content (g C m−2)

16000

S03

CB,0

Microbe biomass concentration (mg C g−1 soil C)

  

0.5

L04

CFR,0

Initial amount of fine roots as a fraction of CW,0 (no units)

 

0.2

NA

CCR,0

Initial amount of coarse roots as a fraction of CW,0 (no units)

 

0.2

NA

WS,0

Initial soil moisture content (fraction of WS,c)

0–1

 

WP,0

Initial snow pack (cm water equivalent)

0

NA

Photosynthetic parameters

Amax

Maximum net CO2 assimilation rate (nmol CO2 g−1 leaf biomass s−1)

0–34

 

FAmax

Average daily max photosynthesis as fraction of Amax (no units)

0.76

A96

TMin

Minimum temperature for photosynthesis (°C)

−8 to 8

 

TOpt

Optimum temperature for photosynthesis (°C)

5–30

 

KVPD

Slope of VPD–photosynthesis relationship (kPa−1)

0.01–0.25

 

K

Canopy PPFD extinction coefficient (no units)

0.38–0.62

 

KWUE

VPD–water use efficiency relationship (mg CO2 kPa g−1 H2O)

0.01–0.25

 

Respiration parameters

KF

Foliar maintenance respiration as a fraction of Amax (no units)

0.05–0.3

 

KW

Wood respiration rate at 0°C (y−1)

0.0006–0.06

 

KH

Soil respiration rate at 0°C and moisture saturated soil (y−1)

0.003–0.6

 

KFR

Fine root respiration rate at 0°C (y−1)

 

0.003–0.6

 

KCR

Coarse root respiration rate at 0°C (y−1)

 

0.003–0.6

 

Q10V

Vegetation respiration Q10 (no units)

1.4–5

 

Q10S

Soil respiration Q10 (no units)

1.4–5

 

Q10FR

Fine root respiration Q10 (no units)

 

1.4–5

 

Q10CR

Coarse root respiration Q10 (no units)

 

1.4–5

 

Allocation parameters

αL

Fraction of mean NPP allocated to leaves (no units)

0.4

S07

αW

Fraction of mean NPP allocated to wood (no units)

 

0.2

NA

αFR

Fraction of mean NPP allocated to fine roots (no units)

 

0.2

NA

αCR

Fraction of mean NPP allocated to coarse roots (no units)

 

(†)

(†)

(†)

NA

βFR

Fine root exudation as a fraction of mean GPP (no units)

 

0.05

NA

βCR

Coarse root exudation as a fraction of mean GPP (no units)

 

0.05

NA

Tree physiological parameters

SLWC

C content of needles on a per-area basis (g C m−2 leaf area)

270

JS

FC

Fractional C content of leaves (g C g−1 leaf biomass)

0.45

A95

Water-related parameters

WS,c

Soil water holding capacity (cm water equivalent)

0.1–36

 

fE

Fraction of water immediately evaporated (no units)

0.1

A92

fD

Fraction of water entering soil, that is immediately drained (no units)

0.1

A92

δS

Snow melt rate (cm water equivalent °C−1 day−1)

0.15

A92

Rd

Scalar relating aerodynamic resistance to wind speed (no units)

36.5

S07

Rsoil,1

Scalar relating soil resistance to soil wetness (no units)

8.2

S96

Rsoil,2

Scalar relating soil resistance to soil wetness (no units)

4.3

S96

TS

Soil temperature at which photosynthesis and foliar respiration are shut down (°C)

−5 to 5

 

f

Fraction of water removable in a timestep (no units)

0.001–0.16

 

fS

Fraction of water available to vegetation in frozen soils (no units)

0

 

Turnover parameters

δL

Turnover rate of leaf C (y−1)

0.001–1

 

δW

Turnover rate of wood C (y−1)

0.001–1

 

δCR

Turnover rate of coarse root C (y−1)

 

0.001–1

 

δFR

Turnover rate of fine root C (y−1)

 

0.001–1

 

Soil quality parameters

qL

Leaf quality (unitless)

  

0.7

NA

qW

Wood quality (unitless)

  

0.3

NA

Microbe parameters

μmax

Microbial maximum ingestion rate (h −1)

  

0.04

L07

Number of estimated parameters (■)

17

23

23

  

The ranges assume a uniform prior distribution.

□: Fixed parameter.

■: Estimated parameter.

†: αCR is equal to 1 − (αL + αW + αFR).

Sources are: A92, Aber and Federer (1992); A96, Aber and others (1996); L04, Lipson and Schmidt ( 2004); L07, Lipson and others (In review); M02, Monson and others (2002); S03, Scott-Denton and others (2003); S07, Sacks and others (2007); S96, Sellers and others (1996).

For this study we modified the soil respiration calculations to model winter CO2 fluxes more accurately. Previous studies (Braswell and others 2005; Sacks and others 2006, 2007) reduced soil respiration at all times of the year by a factor proportional to soil wetness. For this study, we applied this modification only when the soil temperature was greater than 0°C.

The most significant changes to SIPNET are explicit modelling of root carbon dynamics and modelling the influence of soil microbes on the soil carbon pool. Model parameters are determined from literature values or estimated with the model-data fusion routine described in section “Parameter Estimation Routine”. The various model structures are described in detail below and are conceptually shown in Figure 1. Table 2 lists the fixed and estimated parameters for each model modification.
https://static-content.springer.com/image/art%3A10.1007%2Fs10021-007-9120-1/MediaObjects/10021_2007_9120_Fig1_HTML.gif
Figure 1.

SIPNET pools and fluxes for carbon. Photosynthesis, respiration, and allocation fluxes are denoted with dashed lines. Turnover fluxes are denoted with solid lines.

Base Model

This model is the same one used in (Sacks and others 2006, 2007) and is shown in Figure 1A. No explicit modelling of root or soil microbial dynamics occurs. The only allocation to new biomass is to the leaf carbon pool. Wood and leaf respiratory losses are modelled with the following equation:
$$ R_{X} = K_{X} C_{X} \; Q10_{X}^{T_{{\text{air}}}/10}, $$
(1)
where RX is the actual respiration rate from pool X (g C m−2 day−1), KX a base rate (day−1), CX the amount of carbon in a given pool (g C m−2). Needle and wood respiration use the same Q10 value. For needle respiration, the base respiration rate is adjusted by a factor of \(Q_{10}^{-T_{{\text{Opt}}}/10},\) where TOpt is an optimum temperature for photosynthesis (Aber and Federer 1992; Aber and others 1996). Soil heterotrophic respiration is treated as in equation (1), except that soil temperature is used instead of air temperature and respiration is reduced by a factor proportional to the fractional soil wetness when soil temperatures are above zero:
$$ R_{\text{Soil}} =\left\{\begin{array}{ll} K_{\text{S}}C_{\text{S}} \; Q10_{\rm S}^{T_{{\rm Soil}}/10} \left(W_{\text{S}}/W_{{\text{S,C}}} \right) & T_{\text{Soil}} > 0 \\ K_{\text{S}} C_{\text{S}} \; Q10_{\rm S}^{T_{\rm Soil}/10} & T_{\text{Soil}} \leq 0 \end{array}\right.$$
(2)
where RSoil is the actual respiration rate (g C m−2 day−1), KS a base respiration rate (day−1), CS the amount of soil carbon (g C m−2), WS the soil water amount (cm water equivalent), and WS,C is the soil water holding capacity (cm water equivalent). With this formulation of RSoil, heterotrophic respiration (RH) and autotrophic soil respiration are not distinguished.

Roots Model

This model expands on the Base model and is shown in Figure 1B. The wood carbon pool is split into (a) aboveground biomass, (b) fine roots, and (c) coarse roots. Allocation among the four carbon pools (wood, leaves, fine roots, coarse roots) occurs at a rate proportional to the mean NPP over the past 5 days as described in equation (3):
$$ \hbox{Growth allocation to pool}\,X: = \alpha_{X} \overline{\text{NPP}}. $$
(3)
To determine appropriate values for the percentage of NPP allocated to coarse and fine roots (αCR and αFR, respectively), we assume that total belowground carbon allocation (TBCA) is approximately twice litterfall input IL (Raich and Nadelhoffer 1989). Assuming that TBCA is equal to (αCR + αFR)NPP, the sum of αCR and αFR can be found if litterfall inputs are known:
$$ \begin{aligned} {\text{TBCA}} &= 2 I_{\text{L}} = (\alpha_{\text{CR}}+\alpha_{\text{FR}}) {\text{NPP}} \\ \alpha_{\text{CR}}+\alpha_{\text{FR}} &= \frac{2 I_{\text{L}}}{{\text{NPP}}}. \end{aligned} $$
(4)
Litterfall rates (IL) and NPP derived from the Base model provide an estimate for αCR + αFR in equation (4). Examining the frequency distribution of αCR + αFR showed that the most frequent value of αCR + αFR is approximately 0.4 (results not shown). Assuming that this belowground allocation is split equally between fine and coarse roots (McDowell and others 2001; Joslin and others 2006), this yields values of αCR and αFR to be 0.2.

Fine and coarse root respiratory losses (RFine-Root and RCoarse-Root, respectively) are modelled with equation (1) using soil temperature for the Q10 functional response. Heterotrophic respiration RH is modelled with equation (2). Overall soil respiration RSoil equals the sum of RFine-Root, RCoarse-Root, and RH.

In addition to respiration, root carbon losses also occur through exudation into the soil. Root exudation occurs at a rate proportional (βX) to the mean photosynthesis over the past 5 days:
$$ \hbox{Root exudation from pool}\,X: = \beta_{X} \overline{{\text{GEE}}}. $$
(5)

Quality Model

This model is shown in Figure 1C and expands the Roots model by structuring the soil carbon pool into a discrete number of soil pools that theoretically represent a continuum between more labile (high substrate quality, easily decomposed) to more recalcitrant (low substrate quality, less easily decomposed) pools of carbon. For this study, the number of soil carbon pools was fixed at three. These pools are parameterized by a variable q representing the “quality” of a particular pool (Ågren and Bosatta 1987, 1996; Bosatta and Ågren 1991). For this application, the variable q takes on values between zero and one (Bosatta and Ågren 1985). Higher values of q represent more labile soil carbon and lower values more recalcitrant soil carbon.

Variation in the dynamics of each soil pool occurs by associating inputs such as litter with different quality pools. For this study, leaf litter and root exudates enter the highest quality pool, and wood litter enters the second highest quality pool. Associating litter or exudates with a particular soil quality pool potentially leads to different sizes of each of the respective soil pools. As respiration is dependent on pool size, we expect variation in the amount of carbon respired across these soil pools.

In addition to litter inputs and respiration losses, decomposition influences soil pool carbon content in the Quality model. This model assumes that in the process of decomposition the quality (q) of carbon that had been decomposed decreases and enters another soil quality pool. Soil carbon of quality qi is incorporated into microbial biomass at the following ingestion rate:
$$ \hbox{ Ingestion rate: } \epsilon \mu_{max}\frac{\tilde{C}_{{\text{B}},0}}{\sum_{j} C_{{\text{S}},j}} C_{{\text{S}},i}, $$
(6)
where ε is the efficiency in converting carbon into biomass (no units), CS,i the soil carbon in quality pool i (g C m−2), μmax the specific microbial ingestion rate (h−1) and \(\tilde{C}_{{\text{B}},0}\) is the average microbial biomass density of carbon (g C m−2). Growth respiration (RGrowth) is given by equation (7):
$$ R_{{\text{Growth}}} = (1- \epsilon ) \mu_{{\text{max}}}\frac{\tilde{C}_{{\text{B}},0}}{\sum_{j} C_{{\text{S}},j}} C_{{\text{S}},i}. $$
(7)
This growth respiration is associated with respiration from the growth of new microbial biomass. Heterotrophic respiration, or maintenance costs from existing soil microbes, is dependent on soil carbon of quality qi. This respiration is characterized with equation (8), where KH is a base respiration rate (day−1):
$$ R_{{\text{H}},i} = \left\{\begin{array}{ll} K_{{\text{H}}}C_{{\text{S}},i} \; Q10_{\text{S}}^{T_{{\rm Soil}}/10}\left(W_{\text{S}}/W_{{\text{S,C}}} \right) & T_{\text{Soil}} > 0\\ K_{{\text{H}}} C_{{\text{S}},i} \;Q10_{\text{S}}^{T_{{\rm Soil}}/10} & T_{\text{Soil}} \leq 0\end{array}\right. $$
(8)
Overall soil respiration consists of root respiration (RFine-Root and RCoarse-Root), growth respiration (RGrowth) and the heterotrophic respiration (RH,i) across all different soil carbon quality pools.

Linear Soil Respiration Models

Each model variant (Base, Roots, and Quality) adds an additional level of structure to soil carbon. We investigated if this additional complexity leads to an over-specification of soil processes by substituting linear relationships describing soil heterotrophic respiration in the Base and Roots models. Rather than having soil heterotrophic respiration dependent on soil carbon pool size (equation (2)), for this model variant soil heterotrophic respiration was modelled by the following function:
$$ R_{{\text{H}}}= \hbox{max} \left[ (a_{0}+a_{1} T_{\text{Soil}}) \frac{W_{\text{S}}}{W_{{\text{S,c}}}},0 \right], $$
(9)
where “max” represents “maximum of” and a0 and a1 represent the parameters characterizing the assumed linear relationship between heterotrophic respiration and soil temperature. A linear function in equation (9) was chosen over more complicated functions to avoid overfitting the data. Equation (9) was substituted for equation (2) in the Base and Roots models, respectively. When equation (9) is used, no explicit modelling of soil carbon dynamics occurs. We refer to a Base and Roots model run using equation (9) for RH as “Base-Linear” and “Roots-Linear”, respectively.

Parameter Estimation Routine

The parameter optimization method used in this study was a variation of the Metropolis algorithm developed by Metropolis and others (1953). A similar parameter estimation routine was used in Braswell and others (2005) and Sacks and others (2006, 2007); here we only describe the relevant details.

Each given model (Base, Roots, Quality, Base-Linear, Roots-Linear) has a set of parameters used to characterize the model (Table 2). Each model has two types of parameters: fixed and estimated. Fixed parameter values are derived from literature or from unpublished data collected at the Niwot Ridge site. Estimated parameters are found from the Metropolis algorithm. Each estimated parameter is given a range of allowable values; usually this range is selected from literature or from conventional knowledge. The probability distribution over the range of every parameter was assumed to be uniform. The parameters were estimated using twice-daily NEE data in the parameter estimation routine.

The parameter estimation routine proceeds by exploring the parameter space to find the parameter set that maximizes the likelihood L:
$$ L=\prod_{i=1}^{n} \frac{1}{\sqrt{2 \pi} \sigma} \exp \left[-\frac{(x_{i}-\eta_{i})^{2}}{2 \sigma^{2}} \right], $$
(10)
where n was the number of data points, xi and ηi are the measured and modelled data and σ is the standard deviation of the data about the model. Values of xi are twice-daily measurements of NEE. This likelihood function assumes that all errors are Gaussian distributed and that the standard deviation σ followed a uniform distribution. As in Braswell and others (2005) and Sacks and others (2006), for this study σ is estimated by finding the value σe that maximizes the likelihood:
$$ \sigma_{{\text{e}}} = \sqrt{\frac{1}{n} \sum_{i=1}^{n} (x_{i}-\eta_{i})^{2}}. $$
(11)
Braswell and others (2005) used synthetic data sets with different values of σ and found that σe did, in fact, seem to reproduce the σ used to generate a synthetic data set.
At each time step, the current parameter set generates estimates of GEE, aboveground leaf respiration (RL) and wood respiration (RW), and RSoil. These fluxes then determine modelled values of NEE via equation (12), which is then used for ηi in equation (10):
$$ \hbox{NEE} =\hbox{GEE}-R_{{\text{L}}}-R_{{\text{W}}}-R_{\text{Soil}} $$
(12)

Both measured and modelled values of NEE characterize the likelihood (equation (10)). The Metropolis algorithm then proceeds to find the best parameter set that maximizes the likelihood. In the implementation of the Metropolis algorithm we use the log-likelihood because it is mathematically and computationally easier to determine.

The parameter optimization proceeds by randomly selecting a particular parameter, changing its value by a random amount, and evaluating the log-likelihood with this proposed (new) parameter set. If this proposed parameter set increases the log-likelihood, then this parameter set is accepted. If the proposed parameter set did not increase the log-likelihood, it is still accepted with a probability equal to the difference of the log-likelihoods. After a suitable spin-up period, the collection of accepted parameter sets characterizes the joint posterior probability distribution of the parameters (Hurtt and Armstrong 1996; Braswell and others 2005). For a particular parameter, statistics from the frequency distribution of accepted values (typically 150,000 values) determines final parameter statistics.

Past studies with SIPNET (Braswell and others 2005; Sacks and others 2006, 2007) estimated parameters by using the entire available record of flux measurements in the optimization. This approach makes it difficult to evaluate model performance because parameters have already been optimized to match measured data. As a result, for this study we partition the data into two periods: the first 3 years of flux measurements from Niwot Ridge (November 1, 1998 to December 31, 2001) are used in the parameter estimation routine. This set of flux data will be referred to as the “optimization period.” The remainder of the unused data (January 1, 2002 to December 31, 2005) is subsequently used to evaluate the different models. This set of data will be referred to as the “corroboration period.” Mean cumulative annual NEE from 1999 to 2001 (optimization data) was −73 g C m−2, ranging from −49 to −89 g C m−2. For the corroboration period (2002–2005), mean cumulative annual NEE was −60 g C m−2, ranging from −21 to −88 g C m−2. When the year of lowest net CO2 uptake (−21 g C m−2 during 2002) is excluded from the corroboration period, mean cumulative annual NEE was −72 g C m−2 and ranged from −62 to −88 g C m−2.

Results

The parameter set that yielded the highest log-likelihood in the parameter estimation for each model variation (Base, Roots, Quality) is shown in Table 3. In addition, the mean and standard deviation generated from the set of accepted parameter values are reported. Three types of behavior characterize the posterior distributions. Well-constrained parameters are ones where the best and mean values are similar and the standard deviation is typically small (for example, AMax, TMin, K). An edge-hitting parameter is one where the best or mean value is near the edge of its allowed range (for example, KH). Finally, a noninformative parameter is one where the best and mean values differed significantly and the parameter standard deviation is quite large (for example, δW, δCR). A noninformative parameter suggests the NEE data used in the parameter optimization could not constrain that particular parameter. Some parameters have remarkable consistency among the Base, Roots, and Quality models (for example, AMax and TMin), whereas others have considerable variation (for example, δCR and Q10CR).
Table 3.

Retrieved Parameters for Each Model Optimization

Parameter

Model

Base

Roots

Quality

Well-constrained parameters

AMax (nmol CO2 g−1 leaf biomass s−1)

4.5 (4.5 ± 0.2)

4.2 (4.5 ± 0.2)

4.2 (4.5 ± 0.2)

TMin (°C)

−3.0 (−3.0 ± 0.3)

−3.0 (−3.1 ± 0.3)

−3.0 (−3.1 ± 0.4)

TOpt (°C)

14.7 (15.3 ± 0.8)

16.3 (16.6 ± 1.0)

17.0 (16.8 ± 1.1)

KVPD (kPa−1)

0.119 (0.125 ± 0.009)

0.120 (0.126 ± 0.009)

0.119 (0.127 ± 0.009)

K (no units)

5.8 (6.1 ± 0.6)

5.8 (6.0 ± 0.6)

5.3 (6.1 ± 0.7)

KWUE (mg CO2 kPa g−1 H2O)

94.8 (83.8 ± 15.7)

85.0 (72.1 ± 15.9)

98.8 (79.2 ± 17.5)

KF (no units)

0.13 (0.14 ± 0.02)

0.22 (0.20 ± 0.03)

0.23 (0.20 ± 0.03)

Q10V (no units)

1.6 (1.6 ± 0.1)

2.1 (1.9 ± 0.2)

2.2 (1.9 ± 0.2)

WS,c (cm water equivalent)

3.5 (3.6 ± 0.2)

3.6 (3.9 ± 0.2)

3.6 (3.8 ± 0.2)

TS (°C)

0.06 (0.07 ± 0.01)

0.06 (0.07 ± 0.01)

0.06 (0.07 ± 0.01)

f (no units)

0.04 (0.05 ± 0.01)

0.05 (0.05 ± 0.01)

0.04 (0.05 ± 0.01)

Edge-hitting parameters

KW (y−1)

0.023 (0.023 ± 0.003)

0.001 (0.006 ± 0.004)

0.003 (0.007 ± 0.005)

KH (y−1)

0.006 (0.006 ± 0.001)

0.004 (0.004 ± 0.001)

0.003 (0.004 ± 0.001)

Q10S (no units)

5.0 (4.3 ± 0.6)

4.8 (3.5 ± 0.9)

4.6 (3.7 ± 0.8)

Non-informative parameters

WS,0 (fraction of WS,c)

0.83 (0.49 ± 0.29)

0.42 (0.48 ± 0.29)

0.70 (0.49 ± 0.29)

KFR (y−1)

 

0.016 (0.080 ± 0.029)

0.076 (0.065 ± 0.033)

KCR (y−1)

 

0.102 (0.032 ± 0.025)

0.054 (0.045 ± 0.032)

Q10FR (no units)

 

2.9 (1.9 ± 0.6)

1.5 (2.2 ± 0.8)

Q10CR (no units)

 

1.4 (3.0 ± 1.1)

2.0 (2.4 ± 0.9)

δL (y−1)

0.08 (0.08 ± 0.02)

0.07 (0.09 ± 0.02)

0.08 (0.09 ± 0.02)

δW (y−1)

0.002 (0.04 ± 0.03)

0.02 (0.40 ± 0.30)

0.49 (0.36 ± 0.30)

δFR (y−1)

 

0.03 (0.06 ± 0.10)

0.002 (0.10 ± 0.15)

δCR (y−1)

 

0.01 (0.23 ± 0.22)

0.02 (0.20 ± 0.25)

The best value reports the parameter set that yielded the highest likelihood in the parameter estimation. The posterior mean and standard deviation determined from the distribution of the set of accepted parameter values follows in parentheses. Well-constrained parameters are ones where the best and mean values are similar and the standard deviation is small. An edge-hitting parameter is one where the best or mean value is near the edge of its allowed range. A noninformative parameter is one where the best and mean values differed significantly and the parameter standard deviation is quite large.

Table 4 compares the log-likelihood for each of the models using the best parameter set retrieved from the parameter estimation. A higher log likelihood (closer to zero) indicates the model has a better fit with the data. The Roots and Quality models increased the overall log-likelihood from the Base model with the maximum improvement (highest log-likelihood) in the Roots model. With each model refinement (Roots and Quality models), additional parameters are introduced. Introducing these parameters to the model increases the degrees of freedom and may lead to a higher log-likelihood by overfitting the data. Hence, one must ask if the increased log-likelihood associated with the Roots and Quality models truly represents a better model or is an overfit of the data. The Bayesian Information Criterion (BIC) (Schwartz 1978) assesses this by introducing a penalty for each additional parameter:
$$ \hbox{BIC} = -2 {\hbox{LL}} + M\,\hbox{ln} (n), $$
(13)
where n is the number of data points used in the optimization, M is the number of estimated parameters, and LL is the log-likelihood. A lower value of BIC indicates greater support for the model from the data (Kendall and Ord 1990). Values of the BIC in Table 4 indicate that the Roots model had the greatest support from the data.
Table 4.

Model Comparisons Using the Estimated Parameter Set Retrieved from Each Model Run

Model

Base

Roots

Quality

Base-Linear

Roots-Linear

Log likelihood (LL)

−2084.6

−2048.1

−2054.8

−3960.6

−2313.7

NEE root mean square error

0.62

0.61

0.61

1.43

0.69

Number of data points (n)

2230

2230

2230

2230

2230

Number of parameters (M)

17

23

23

23

23

\(\hbox{BIC}^{\dag}\)

4300

4274

4287

8099

4805

Data from the corroboration period were used to calculate these values. The root mean square error is calculated from the squared difference between the measured and modelled difference for NEE. \((\dag):\) The Bayesian Information Criterion (BIC) equals −2LL + M ln(n). A lower BIC indicates a model with greater support from the data.

Figure 2 compares measured NEE to modelled NEE for the Quality model using the best (for example, highest likelihood) parameter set and data from the corroboration period. Similar results for the other models were obtained and hence are not shown. Figure 2 distinguishes between winter and summer time periods. For each year, summer was determined by the zero crossing of daily integrated NEE, indicating an ecosystem transition from a net source of CO2 to a net sink of CO2.
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Figure 2.

Comparison of measured and modelled NEE fluxes using the corroboration data for the Quality model. Winter and summer are distinguished by a zero crossing of daily integrated NEE for a given year.

During the winter, the Quality model predicts more net CO2 uptake (more negative NEE) than observed. During the summer this pattern is reversed, with the model predicting less net uptake (less negative NEE, Figure 2B). Similar results to the patterns in Figure 2 were found in Sacks and others (2006, 2007).

Figure 3 shows estimated values of NEE, GEE and TER for each of the model variants. Clearly, all models are able to generate consistent estimates of GEE and TER. Figure 4A shows the twice daily values of measured and modelled NEE for the Roots model. Examination of the difference between measured and modelled cumulative NEE (Figure 4B) shows marked differences between the Base, Roots, and Quality models. Although all models correctly show that the ecosystem is a net sink of CO2, they differ in their predictions of the size of this sink. The Base model eventually predicts less cumulative net uptake than the Quality or Roots models. All models predict similar levels of photosynthesis but have different respiration rates (Figure 3). Similar levels of photosynthesis are a consequence of generating similar values for photosynthetic parameters in the estimation routine (Table 3). If data were being overfitted, there is no prior reason to expect this robustness in the photosynthetic parameters. Additionally, from Figure 4B the Roots model underestimates respiration, whereas the Base and Quality models overestimate respiration. No model could capture the decreases in net CO2 uptake caused by drought during the summer of 2002 (Figure 3E).
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Figure 3.

Comparison of modelled GEE, TER, and NEE for each of the model variants. Values shown are a running 28-day mean for the corroboration period only.

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Figure 4.

Comparisons of measured and modelled cumulative NEE. Panel (A) shows comparison among twice-daily values of measured NEE and modelled NEE for the Roots model. Similar results for the other model variants were obtained. Panel (B) shows the difference between measured and modelled values of cumulative NEE for each of the model variants. Positive values indicate that the model is producing more negative values of NEE than measurements. Gray-shaded panels in both plots represent the optimization period of fluxes used to estimate model parameters.

Figure 5 shows values of RSoil (Figure 5A–C), RRoot (Figure 5D, E) and RH (Figure 5F, G) for each of the model variants. Note that the Base model does not model root dynamics, hence RRoot and RH are subsumed into RSoil. Estimates of RRoot for the Roots and Quality models all reached a maximum during summer months. This summer peak in root respiration agrees with seasonal trends shown in Bond-Lamberty and others (2004b). Model estimates of RH show summer-time decreases in the Roots and Quality models. These decreases are attributed to decreases in soil moisture, which reduce the amount of respiration. Suppression of heterotrophic, but not root, respiration during periods of soil moisture limitations is consistent with observations reported by Scott-Denton and others (2006).
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Figure 5.

Comparison of modelled soil respiration fluxes for each of the model variants. Values shown are a running 28-day mean for the corroboration period. RRoot and RH are not a component of the Base model.

Figure 6 shows the distribution of values of RSoil/TER and RRoot/RSoil for each of the model variants. The Roots and Quality models have seasonal variation in the contribution of RSoil to TER and RRoot to RSoil, with wintertime values having RSoil/TER closer to unity. This seasonal variation arises from the assumption that foliar respiration only occurs when the air temperature is above a certain threshold, TS, which for the Base, Roots, and Quality models was estimated to be 0.06°C; thus, in the parameter estimation routine all ecosystem respiration is forced toward RRoot and RSoil during the winter.
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Figure 6.

Histograms of the contribution of RSoil to TER (panels AC) or RRoot to TER (panels D, E) for each of the model variants during the corroboration period. RRoot and RH are not a component of the Base model.

Discussion

Overall Model Comparisons

The models produce reasonable values of NEE that corresponded well with measurements (Figure 4A). Overall, these soil carbon models did not detract from the ability of SIPNET to partition NEE into GEE and TER (Figure 3).

Variation in the long-term modelled NEE (Figure 4B) between the Base, Roots, and Quality models is strongly dependent on the assumptions governing each model and the values of the parameters estimated from the data assimilation routine. As estimated photosynthetic parameters between the models were quite robust, variation in long-term modelled NEE is a consequence of the lack of robustness in parameters describing turnover and respiration rates between the Base, Roots, and Quality models. Higher values of base respiratory rate parameters (for example, KH, KCR, KFR) would increase overall respiration rates. A higher pool turnover rate would reduce the amount of carbon in a particular pool. As respiration rates are assumed to be proportional to pool size, variation in turnover rate parameters indirectly affect respiratory fluxes and ultimately modelled NEE values.

The model with the lowest BIC is the Roots model (Table 4). The penalty for each additional parameter (the value of ln(n) in equation (13)) is approximately 8. Arguably the lower BIC from the Roots model is a marginal improvement over the Base and Quality models (approximately 1% from the Base model). The Roots and Quality models have at least 6 more additional parameters than the Base model. If some of these additional parameters could be determined from direct experimentation, this would reduce the value of the BIC for the Roots and Quality and make the BIC comparison more robust.

Estimation of Soil Respiration Fluxes

A given model structure can have significant effects on modelled soil respiration fluxes (Figure 5 and Table 3). Past studies with SIPNET have been able to successfully partition NEE into GEE and TER (Braswell and others 2005; Sacks and others 2006, 2007), but had less success in partitioning TER into its autotrophic and heterotrophic components. Inclusion of root carbon pools, and structuring the soil carbon through a soil quality approach show improvements in the ability to match measured CO2 fluxes with the Roots and Quality models having higher log-likelihoods than the Base model (Table 4).

The estimated contribution of soil respiration to total ecosystem respiration (RSoil/TER) predicted by the various models presented in this study can be compared to previously published studies (Table 5). Mean values as an average across the corroboration period are reported, however, we note that seasonal variation in soil respiration fluxes was found in the Roots and Quality models (Figure 6). Model predicted values of RSoil/TER for the Roots and Quality models all fall within ranges of published studies at Niwot Ridge (Monson and others 2006a) or other literature studies (Lavigne and others 1997; Law and others 1999; Janssens and others 2001; Davidson and others 2006b). Note that the Base model significantly underestimates RSoil/TER. The mean values reported in Table 5 may be biased toward wintertime values, which were generally close to unity for the Roots and Quality models (Figure 6B, C). We argue these modelled values are overestimated; Monson and others (2006a) estimated wintertime values of RSoil/TER at Niwot Ridge to be 0.35–0.48. As discussed in section “Results”, these large values of wintertime RSoil/TER reflect the model assumption that foliar respiration is zero below a temperature threshold.
Table 5.

Comparison of Estimated Respiration Components to Literature Values

Parameter

Model/Literature reference

Value

Notes

RSoil/TER

Base

0.18 (0.02–0.28)

 

Roots

0.64 (0.35–0.98)

 

Quality

0.69 (0.39–0.98)

 

Monson and others (2006a)

0.35–0.7

Niwot Ridge study

Law and others (1999)

0.76

Ponderosa pine forest

Janssens and others (2001)

0.69 ± 0.35

Average across 18 Euroflux sites

Lavigne and others (1997)

0.48–0.71

Range across six coniferous boreal sites

Davidson and others (2006b)

0.5–0.8

 

RRoot/RSoil

Base

N/A

 

Roots

0.78 (0.63–0.92)

 

Quality

0.83 (0.71–0.94)

 

Hanson and others (2000)

0.1–0.9

Review of published studies

Högberg and others (2001); Bhupinderpal-Singh and others (2003)

0.5–0.65

Forest girdling study

Bond-Lamberty and others (2004a)

0.3–0.5

Review of published studies from 54 sites

Bond-Lamberty and others (2004b)

0.05–0.4

Study across a black spruce chronosequence

Subke and others (2006)

0.3–0.6

Meta-analytical review of published studies

Wang and Yang (2007)

0.5–0.8

Range across six temperature forests

Carbone and others (2007)

0.2 ± 0.03

14C pulse-labeling study

Modelled values are given as a mean across the corroboration period followed by the 10–90% range of the parameter values.

Modelled values of the contribution of RRoot to RSoil are approximately 0.8, with considerable variation (Table 5). These values are significantly higher than those reported from girdling studies at Niwot Ridge (0.4–0.5, Scott-Denton and others (2006)) and in literature. A recent meta-analysis by Subke and others (2006) showed that the contribution of heterotrophic respiration to soil respiration ranged between 0.4–0.7, implying that the contribution of RRoot to RSoil is approximately 0.3–0.6. Variation in this ratio may depend on forest age (Bond-Lamberty and others 2004b), time of year (Bond-Lamberty and others 2004b), plant phenology (Davidson and others 2006b), litter inputs (Dehlin and others 2006; Cizneros-Dozal and others 2007), nutrient cycling (Brooks and others 2004), or ecosystem type (Subke and others 2006). Methodological differences may have an effect on experimental estimates of RRoot and by association RRoot/RSoil; these are discussed further in Hanson and others (2000), Hendricks and others (2006), Jassal and Black (2006), and Subke and others (2006).

The Roots and Quality models led to better agreement from the Base model in determining the contribution of RSoil to TER (Table 5). In spite of these encouraging results, additional work is needed to further partition RSoil into its constituent components RRoot and RH. Improvements could be made to the model structure by modelling physical and biological effects on winter soil respiration fluxes (Massman and others 1997; Brooks and others 2004; Hubbard and others 2005; Monson and others 2006b). Incorporating these changes to SIPNET could improve the ability to estimate RRoot/RSoil.

The use of linear functions to describe soil heterotrophic respiration (for example, equation (9)) contrasts with more mechanistic descriptions of soil heterotrophic respiration (for example, equations (2) and (8)). Describing soil respiration with a linear functions provides a worse model-data fit (higher BIC, Table 4) and unrealistic estimates of heterotrophic respiration than with mechanistic approaches (results not shown). Often a fitted linear model defines the best a process model can expect to do, suggesting the Base-Linear and Roots-Linear models omit crucial processes. Previous SIPNET studies (for example, Sacks and others (2006, 2007)) and the results from the Roots model suggest that these processes are most likely time-scales and a degree of uncoupling between soil and aboveground processes.

Evaluation of Allocation Parameters and Estimated Turnover Rates

Biomass turnover rate parameters estimated from the various models can be compared to turnover rates from published studies (Table 6). As discussed in section “Results”, leaf turnover rate (δL) is a parameter well-constrained from the data assimilation. When these values are converted to litterfall rates, they compare favorably with literature values. Needle turnover rates in the range of 0.050–0.090 y−1 correspond to leaf litterfall rates of 100–180 g C m−2 y−1, assuming leaf biomass is approximately 900 g C m−2 and the fractional carbon content of leaves is 0.45. For our simulations, the final values of leaf biomass across all model variants range from 900 to 950 g C m−2 (results not shown). Annual litterfall input at Niwot Ridge has been estimated to be 184 g C m−1 y−1 (Sacks and others 2007). These litterfall rates are certainly within the range of values from a variety of ecosystems reported in Davidson and others (2002). Laiho and Prescott (1999) reported annual litterfall input for A. lasiocarpa and P. englemanii forests to be 200 and 240 g C m−2 y−1, respectively. Assuming that half of the litter is foliage, this would correspond to leaf litter input rates of 100–120 g C m−2 y−1.
Table 6.

Comparison of Estimated Turnover Rate Parameters to Literature Values

Parameter

Model/Literature reference

Value

Notes

δL (y−1)

Base

0.08

 

Roots

0.07

 

Quality

0.08

 

Laiho and Prescott (1999)

\(0.051{-}0.058 (\dag)\)

Separate P. englemanni and A. lasiocarpa study site

δW (y−1)

Base

0.002

 

Roots

0.02

 

Quality

0.49

 

Laiho and Prescott (1999)

\(0.009-0.01 (\dag)\)

Separate P. englemanni and A. lasiocarpa study site

δCR (y−1)

Base

N/A

 

Roots

0.01

 

Quality

0.02

 

Arthur and Fahey (1992)

0.056

Mixed P. englemanni and A. lasiocarpa forest

δFR (y−1)

Base

N/A

 

Roots

0.03

 

Quality

0.002

 

Arthur and Fahey (1992)

0.137

Mixed P. englemanni and A. lasiocarpa forest

\((\dag):\) Derived from reported litterfall of 205 g m−2 y −1 for A. lasiocarpa and 235 g m−2 y−1 for P. englemanni, assuming that 50% of litter was needles and leaves (Laiho and Prescott1999). This number was then multiplied by the fractional carbon content of leaves (0.45) and wood (0.5) and dividing by leaf and wood biomass (assumed to be 900 and 5500 g C m−2, respectively).

The wood turnover rate parameter (δW) is not well-constrained for any of the model variants. Assuming wood biomass is 5500 g C m−2 and a fractional carbon content of 0.5 (Laiho and Prescott 1999), then wood turnover rates of 0.01–0.04 y−1 correspond to wood litterfall rates of 110–440 g C m−2 y−1. Woody litterfall input ranges derived from reported values in Laiho and Prescott (2004) were 100–120 g C m−2 y−1; these measured values are near the low end of the modelled ranges. Hence, we can conclude that estimated values of δW for the Roots and Quality models may be too high. With these high values of δW, simulations of the Quality model predicted a much lower final pool size for wood biomass (<1000 g C m−2) then would be expected in the context of the above studies.

Estimated fine and coarse root turnover rates have considerable variation among each of the model variants, suggesting that NEE data alone could not adequately constrain these parameters. We would not have any prior reason to suspect that half-daily NEE data could constrain these parameters, as wood and roots require several months to years to decompose. To obtain a good constraint for these parameters stable isotope or radiocarbon approaches (Gaudinksi and others 2001) would be needed. While there is considerable variation in the root turnover parameters, published literature values have considerable variation as well. Gill and Jackson (2000) reviewed 190 published studies and reported root turnover rates in temperate coniferous forests to range from 0.1–0.8 y−1. This variation in turnover rates may arise from methodological biases used to determine these rates (Hendricks and others 2006; Subke and others 2006).

The considerable variation in the estimated turnover parameters may reflect the simplistic way SIPNET treats turnover of particular carbon pools. Turnover rate parameters represent not only loss from a particular carbon pool as litter, but also subsequent decay and release of that carbon into the soil carbon pool. Decay and subsequent release into the soil typically occurs at a much slower rate than litterfall, which would decrease the value of a particular turnover parameter. Reported decay values in coniferous forests are much lower than input rates (Johnson and Greene 1991; Laiho and Prescott 2004).

This study assumes a constant allocation to roots, leaves, and wood. This constant allocation assumption has broad support in the literature (Raich and Nadelhoffer 1989; Bond-Lamberty and others 2004a; Hendricks and others 2006; Subke and others 2006). We derived values of αCR and αFR from an assumed relationship between TBCA and litterfall rate (Raich and Nadelhoffer 1989). This relationship has been found to be highly uncertain, and perhaps larger, for forests not at steady state (Davidson and others 2002). Niwot Ridge is recovering from early twentieth-century logging (Monson and others 2002); hence applying the relationship from Raich and Nadelhoffer (1989) may underestimate αCR and αFR.

We chose a 5-day time period between photosynthesis and structural allocation of carbon. This argues that there is a 5-day lag between recently assimilated carbon to when it could potentially be respired. Past studies using (a) stable isotope tracers (Ekblad and Högberg 2001; Bowling and others 2002; Knohl and others 2005; Schaeffer and others In press), (b) tree girdling to remove photosynthate supply (Högberg and others 2001), (c) radiocarbon tracing techniques (Carbone and others 2007), or (d) soil CO2 measurements combined with measurements of NEE (Tang and others 2005a) have estimated this lag to vary from 1 to 10 days. Hence, our choice of a 5-day lag is appropriate but highly uncertain.

This study assumed that carbon exudates from the rhizosphere into the soil are proportional to mean GEE over the past 5 days. The 5-day lag and proportionality constants (βFR and βCR) are conservative estimates from field studies (Jakobsen and Rosendahl 1990; Rangel-Castro and others 2005; Christensen and others 2007; Kaštovská and Šantr
https://static-content.springer.com/image/art%3A10.1007%2Fs10021-007-9120-1/MediaObjects/10021_2007_9120_Figa_HTML.gif
čkova 2007); these values are highly uncertain and are strongly dependent on soil substrate quality and microbiota (Kaštovská and Šantr
https://static-content.springer.com/image/art%3A10.1007%2Fs10021-007-9120-1/MediaObjects/10021_2007_9120_Figb_HTML.gif
čkova 2007).

Evaluation of Quality model

The Quality model presented here is based on a discrete version (Bosatta and Ågren 1985) of a continuous time, continuous quality model (Ågren and Bosatta 1987, 1996; Bosatta and Ågren 1991). Additional complexities for the Quality model could be incorporated. First, previous modelling studies have argued that μmax and ε should be an increasing function of quality (Ågren and Bosatta 1987, 1996; Bosatta and Ågren 1991, 1999). Second, temperature may have an additional effect on soil parameters (Holland and others 2000; Tjoelker and others 2001; Wythers and others 2005; Davidson and Janssens 2006). Inclusion of temperature dependence in the ingestion rate (μmax), efficiency (ε), or Q10 values could generate different results than the ones presented here. Initial data assimilation tests showed that there was not enough information in the flux data to include these additional complexities.

For this study, litter and root exudates are quality dependent, leading to potential differences in the respiration from these different soil quality pools. The assumption of quality-dependent litter is supported in a recent study by Dehlin and others (2006), which found that microbial communities responded differently to mixtures of different substrates than when grown with individual substrates alone. Additionally, for this study, soil is always degraded to a lower quality with no delay between subsequent ingestion and release back to the soil. Subsequent degradation in soil quality may be valid for application of the Quality model on longer timescales (decades to centuries, Ågren and Bosatta (1987)), but may not be appropriate for SIPNET on a twice-daily timestep.

One of the challenges of the soil quality model is parameterizing measurements of soil quality mathematically. The most general definition of quality is the accessibility of a substrate for decomposition (Ågren and Bosatta 1996; Bosatta and Ågren 1999). Alternatively, soil quality may be explicitly parameterized by physical parameters (water content, density), chemical factors (pH, total organic carbon), biological activity (microbial activity, presence of pathogens) (Burns and others 2006), or radiocarbon content (Trumbore 2000). Future studies should explicitly link these additional definitions of soil quality with measurements (for example, soil temperature and moisture).

The microbiota play a critical role and their dynamics reflect community processes, nutrient limitations, and specific substrate effects (Brooks and others 1996; Monson and others 2006b; Scott-Denton and others 2006; Lipson and others In review). None of these influences are explicit to this model. Future model refinements are needed to address these issues.

Future Work

Many estimated parameters from the Roots and Quality models (for example, turnover parameters) were not as well constrained as other parameters, (for example, Amax, Tmin, TOpt). Site-specific determination of these unconstrained parameters can improve upon the results here by reducing the number of degrees of freedom, potentially improving model-data fits. Repeating this analysis with the inclusion of additional data streams in the data assimilation (such as measurements of RSoil appropriately scaled to the ecosystem) might better constrain some of the model parameters. Future studies should also attempt to incorporate in the data optimization more discrete measurements such as litterfall measurements or needle biomass surveys. Such measurements would complement NEE measurements by providing a stronger direct constraint on pool size. Equation (10) would then contain additional terms describing these constraints. The combination of time series data (NEE measurements) with discrete data (RSoil measurements) in the likelihood function will require careful consideration.

Fundamental to the approach of SIPNET is the introduction of additional complexity only when needed to avoid overfitting data. The Roots and Quality models increase confidence in the ability of SIPNET to characterize soil respiration at the ecosystem scale when compared to the Base SIPNET model or linear models of soil respiration. However, additional modifications such as site-specific determination of soil pool turnover parameters and consideration of multiple resource limitations are needed. Yet we stress that this conclusion could not have been reached if a more complicated model was initially used. Furthermore, ecosystem-scale RSoil measurements would provide additional comparisons to potentially strengthen our conclusions. This could be achieved with plot-level measurements of RSoil, however care must be exercised when scaling these plot-level RSoil values to the ecosystem (Lavigne and others 1997; Dore and others 2003).

Conclusions

This study modified an established process-based ecosystem model and evaluated contrasting models of soil carbon processes. Comparisons of the original model to model refinements found no noticeable difference in model predictions of GEE and TER. However, these model refinements strongly diverged from the original model in their estimates of soil respiration fluxes.

Results from this study strongly conclude that the NEE flux alone is not a strong constraint on soil fluxes. Modifications to the basic model structure of SIPNET by adding explicit dynamics to the root and heterotrophic components helped, but introduced additional complexities.

This study found that mechanistic representations of soil heterotrophic respiration are better than using a fitted linear model. This is strong evidence that the structure of the soil ecosystem (roots, soil organic matter quality) have direct and first-order effects on fluxes that can not be captured in a parametric zeroth or simple first order regression model.

Therefore, extracting information about the environmental controls on the fluxes requires (a) the correct model structure (which will be even somewhat more complex than presented here) and (b) additional data constraining soil processes such as microbial growth efficiency or net and gross nitrogen mineralization.

Acknowledgments

JMZ would like to thank Frederick Adler and Aaron McDonald for helpful discussions. The authors thank Steve Aulenbach for computer support. JMZ was funded as a fellow in the U.S. Department of Energy, Global Change Education Program, administered by the Oak Ridge Institute for Science and Education. WJS was supported by a National Science Foundation Graduate Research Fellowship. Additional funding was provided by a grant to DRB from the Office of Science (BER), U.S. Department of Energy, Grant No. DE-FG02-04ER63904, as part of the North American Carbon Program. Partial support for these studies was provided by funds from the Western Office of the National Institute for Climate Change Research (NICCR) under and agreement with the U.S. Department of Energy (BER Program). The authors would like to thank three anonymous reviewers for improving previous versions of this manuscript.

Copyright information

© Springer Science+Business Media, LLC 2008