Uncertainty analysis of modeled carbon fluxes for a broad-leaved Korean pine mixed forest using a process-based ecosystem model

Abstract

The uncertainty in the predicted values of a process-based terrestrial ecosystem model is as important as the predicted values themselves. However, few studies integrate uncertainty analysis into their modeling of carbon dynamics. In this paper, we conducted a local sensitivity analysis of the model parameters of a process-based ecosystem model at the Chaibaishan broad-leaved Korean pine mixed forest site in 2003–2005. Sixteen parameters were found to affect the annual net ecosystem exchange of CO₂ (NEE) in each of the three years. We combined a Monte Carlo uncertainty analysis with a standardized multiple regression method to distinguish the contributions of the parameters and the initial variables to the output variance. Our results showed that the uncertainties in the modeled annual gross primary production and ecosystem respiration were 5–8% of their mean values, while the uncertainty in the annual NEE was up to 23–37% of the mean value in 2003–2005. Five parameters yielded about 92% of the uncertainty in the modeled annual net ecosystem exchange. Finally, we analyzed the sensitivity of the meteorological data and compared two types of meteorological data and their effects on the estimation of carbon fluxes. Overestimating the relative humidity at a spatial resolution of 10 km × 10 km had a larger effect on the annual gross primary production, ecosystem respiration, and net ecosystem exchange than underestimating precipitation. More attention should be paid to the accurate estimation of sensitive model parameters, driving meteorological data, and the responses of ecosystem processes to environmental variables in the context of global change.

Appendices

Appendix

The CEVSA2 (“carbon exchange between vegetation, soil, and the atmosphere,” version 2) model is a process-based terrestrial ecosystem model that simulates the carbon exchange between vegetation, soil, and the atmosphere by modeling the processes of photosynthesis, respiration, litter production, and decomposition, as controlled by environmental conditions and vegetation characteristics (Cao and Woodward 1998; Gu et al. 2010).

Photosynthesis and gross primary production

Photosynthesis is calculated by a modified Farquhar biochemical model (Harley et al. 1992). The photosynthesis rate of a leaf is determined by the minimum rates of three processes: (1) the rate of carboxylation (W _c, μmol m⁻² s⁻¹), which depends on the amount, kinetic properties, and activation state of ribulose bisphosphate carboxylase–oxygenase (Rubisco); (2) the rate of carboxylation (W _j, μmol m⁻² s⁻¹), as controlled by the rate of ribulose bisphosphate (RuBP) regeneration in the Calvin cycle, and; (3) the rate of carboxylation W _p (μmol m⁻² s⁻¹), which is controlled by the triose phosphate utilization (U, μmol m⁻² s⁻¹). The net rate of CO₂ assimilation (A, μmol m⁻² s⁻¹) is expressed by

$$ A = {\text{min\{}}W_{\text{c}} ,W_{\text{j}} ,W_{\text{p}} {\text{\} }}\left( {1 - 0.5\frac{{P_{\text{o}} }}{{\tau P_{\text{c}} }}} \right) - R_{\text{d}}, $$

(A1)

with

$$ W_{\text{c}} = \frac{{V_{\text{c}}^{ \max } P_{\text{c}} }}{{P_{\text{c}} + K_{\text{c}} (1 + P_{\text{o}} /K_{\text{o}} )}} $$

(A2)

$$ W_{\text{j}} = \frac{{JP_{\text{c}} }}{{4(P_{\text{c}} + P_{\text{o}} /\tau )}} $$

(A3)

$$ W_{\text{p}} = 3U + \frac{{0.5W_{ \min } P_{\text{o}} }}{{\tau P_{\text{c}} }}, $$

(A4)

where P _o (P _a) and P _c (P _a) are the internal partial pressures of O₂ and CO₂ respectively, τ (J mol⁻¹) is the specificity factor of Rubisco for CO₂ relative to O₂, R _d (μmol m⁻² s⁻¹) is the rate of respiration in light due to processes other than photorespiration, V ^max_c (μmol m⁻² s⁻¹) is the maximum rate of carboxylation by Rubisco, J (μmol electrons m⁻² s⁻¹) is the rate of electron transport, and W _min (μmol m⁻² s⁻¹) is the minimum of W _c and W _j.

V ^max_c is derived from Eq. A2 when the light-saturated rate of photosynthesis is maximized, which depends on the plant nitrogen uptake N _p (μmol m⁻² g⁻¹ day⁻¹):

$$ A_{\max } = \frac{{190N_{\text{p}} }}{{360 + N_{\text{p}} }}, $$

(A5)

where the plant nitrogen uptake N _p is expressed by an empirical function of soil carbon and nitrogen content:

$$ N_{\text{p}} = 120\,{\text{min\{}}s_{\text{n}} /600,1{\text{\} e}}^{{ - 8 \times 10^{ - 5} s_{\text{c}} }} f_{\text{N}} (T)f_{\text{N}} (w_{\text{s}} ). $$

(A6)

The temperature response of the nitrogen uptake is based on the concept of the activation energy required for a process (Jones 1992). The soil moisture response of the nitrogen uptake is expressed by the ratio of soil moisture to soil water holding capacity,

$$ f_{\text{N}} (w_{s} ) = \frac{{w_{\text{s}} }}{{W_{\text{c}} }}. $$

(A7)

The electron transport rate J is driven by the radiation absorbed by the canopy I (μmol photons m⁻² s⁻¹),

$$ J = \frac{\alpha I}{{\sqrt {1 + \frac{{\alpha^{2} I^{2} }}{{J_{ \max }^{2} }}} }}, $$

(A8)

where α is the efficiency of light conversion, and J _max (μmol electrons m⁻² s⁻¹) is the light-saturated rate of electron transport, which is linear with V ^max_c . The photosynthesis rate is limited by the stomatal conductance to water vapor (g _s, mmol m⁻² s⁻¹),

$$ A = \frac{{g_{\text{s}} }}{160}(P_{\text{a}} - P_{\text{c}} ), $$

(A9)

where P _a (P _a) is the atmospheric partial pressure.

The stomatal conductance (g _s) is calculated by a modified Ball–Berry stomatal conductance model (Woodward et al. 1995):

$$ g_{\text{s}} = (g_{0} + g_{1} AR_{\text{h}} /P_{\text{a}} )f(w_{\text{s}} ), $$

(A10)

where g ₀ (mmol m⁻² s⁻¹) is the stomatal conductance when the assimilation rate (A) is zero at the light compensation point, g ₁ is an empirical sensitivity coefficient, and f(w _s) is the response function of stomatal conductance to soil water content (w _s, g g⁻¹), which is defined by a hyperbolic response function (Woodward et al. 1995) based on data presented in Gollan et al. (1992):

$$ f(w_{\text{s}} ) = \frac{{s_{1} (w_{\text{s}} - s_{0} )}}{{w_{\text{s}} - 2s_{0} + s_{2} }}, $$

(A11)

where s ₀ (g g⁻¹) is the value of the soil water content at which stomatal conductance is zero, s ₁ is a response parameter for stomatal conductance, representing the slope of the response of the conductance to increases in soil water content above s ₀, and s ₂ (g g⁻¹) is the value of the soil water content above which the conductance response flattens.

The canopy is divided into several layers according to leaf area index (LAI). The number of layers is equal to the leaf area index of the canopy. The irradiance absorbed by the canopy I is calculated from Beer’s law:

$$ I = I_{0} {\text{e}}^{ - kLAI}, $$

(A12)

where I ₀ (μmol photons m⁻² s⁻¹) is the incident irradiance on the canopy and k is the light extinction coefficient.

Gross primary production is calculated as the sum of the production via photosynthesis in various layers:

$$ {\text{GPP}} = \sum\limits_{i} {A_{i} }. $$

(A13)

Autotrophic respiration

The R _a in CEVSA2 (R _a, μmol m⁻² s⁻¹) is the sum of the maintenance respiration (R _m, μmol m⁻² s⁻¹) and growth respiration (R _g, μmol m⁻² s⁻¹). The foliar maintenance respiration rate R _mf (μmol m⁻² s⁻¹) depends on the nitrogen uptake N _p and the temperature T _k (K):

$$ R_{\text{mf}} = \frac{{N_{\text{p}} }}{50}{\text{e}}^{{r_{1} - \frac{{r_{2} }}{{8.3144T_{k} }}}}, $$

(A14)

where r ₁ and r ₂ are the response functions of the foliar maintenance respiration rate to temperature.

The respiration to maintain tissue other than leaves R _mw (μmol m⁻² s⁻¹) depends on the mass of living tissue m _w (μmol m⁻²) and the temperature T _k:

$$ R_{\text{mw}} = k_{\text{m}} m_{\text{w}} R(T_{k} ), $$

(A15)

where k _m (s⁻¹) is the maintenance respiration coefficient, and R(T _k) is the temperature response function for the maintenance respiration of tissue other than leaves, expressed by

$$ R(T_{k} ) = {\text{e}}^{{21.6 - \frac{{5.367 \times 10^{4} }}{{8.3144T_{k} }}}}. $$

(A16)

The mass of living tissue other than leaves m _w is

$$ m_{\text{w}} = L_{ \max } h/0.89, $$

(A17)

where the canopy height h (m) is derived from a simple function of the maximum leaf area index (Shugart 1984),

$$ h = 0.807L_{ \max }^{2.137}. $$

(A18)

The growth respiration is estimated to be proportional to the difference between the GPP (g C m⁻²) and maintenance respiration:

$$ R_{\text{g}} = f({\text{GPP}} - R_{\text{m}} ), $$

(A19)

where f is the ratio of growth respiration to the difference between photosynthesis and maintenance respiration.

Carbon allocation and litter

Net primary production (NPP, g C m⁻²) is defined as the difference between GPP and plant R _a:

$$ {\text{NPP}} = {\text{GPP}} - R_{\text{a}}. $$

(A20)

Net primary production is allocated to leaves (C _L, g C m⁻²), stems (C _S, g C m⁻²), and roots (C _R, g C m⁻²):

$$ {\text{NPP}} = C_{\text{L}} + C_{\text{S}} + C_{\text{R}} $$

(A21)

The carbon allocation strategy is based on the assumption that ecosystems acclimate to environmental conditions so as to enhance the acquisition of the most limited resources to maintain maximum growth. The allocations of production to stems (a _S), roots (a _R), and leaves (a _L) are calculated as

$$ a_{\text{S}} = \frac{{\varepsilon_{\text{S}} + \omega (1 - L)}}{1 + \omega (2 - L - W)} $$

(A22)

$$ a_{\text{R}} = \frac{{\varepsilon_{\text{R}} + \omega (1 - W)}}{1 + \omega (2 - L - W)} $$

(A23)

$$ a_{\text{L}} = \frac{{\varepsilon_{\text{L}} }}{1 + \omega (2 - L - W)} = 1 - a_{\text{S}} - a_{\text{R}}, $$

(A24)

where ε _S, ε _R, ε _L, and ω are PFT-dependent parameters, and ε _S + ε _R + ε _L = 1, L and W are the light and water availability, respectively.

The plant must have sufficient woody biomass to support the mass of its leaves. Allocations between leaves, stem, and roots maintain the following relationship:

$$ M_{\text{S}} + M_{\text{R}} = \varepsilon M_{\text{L}}^{{k_{\text{a}} }}, $$

(A25)

where M _S (g C m⁻²), M _R (g C m⁻²), and M _L (g C m⁻²) are the carbon in the stem, roots, and leaves, respectively, ε and k _a are PFT-dependent constants.

The increase in the rate of leaf area index at each time step depends on the difference between the production newly allocated to foliage (C _L, g C m⁻²) and the litter production (L _L, g C m⁻²),

$$ \Updelta {\text{LAI}} = \frac{{C_{\text{L}} - L_{\text{L}} }}{S}, $$

(A26)

where S is the specific leaf area (m² g⁻¹).

Litter production is estimated based on plant organ biomass and the mean residence time of each plant organ according to plant phenology. The aboveground litter fall occurs at the end of the growing season in a deciduous forest. For example, foliage litter is calculated by

$$ L_{\text{L}} = \frac{{M_{\text{L}} }}{{R_{\text{L}} }}, $$

(A27)

where M _L is the foliage biomass and R _L is the mean residence time of leaves (days). Root litter shedding is calculated using a similar equation, and lags one month behind the aboveground litter fall.

Heterotrophic respiration and carbon decomposition

The processes of R _h and carbon decomposition are modeled based on the CENTURY model (Parton et al. 1993). Litter entering the soil is decomposed into CO₂ or transferred into soil organic matter, which is finally decomposed into CO₂. Soil organic matter is divided into eight pools: surface structural litter (X ₁), structural root litter (X ₂), soil microbes (X ₃), surface microbes (X ₄), surface metabolic litter (X ₅), metabolic root litter (X ₆), slow soil organic matter (X ₇), and passive soil organic matter (X ₈). The carbon decomposition in these pools is assumed to be a first-order rate reaction influenced by environmental conditions such as temperature, soil moisture, nitrogen availability, soil texture, and the ratio of litter lignin to nitrogen. Heterotrophic respiration is determined as the sum of CO₂ loss:

$$ R_{\text{h}} = \sum\limits_{i = 1}^{8} {X_{i} K_{\text{ai}} F_{i} }, $$

(A28)

where X _i (g C m⁻²) and K _ai (day⁻¹) are the carbon storage and decay rate, respectively, of the soil carbon pool i, and F _i is the fraction of carbon lost due to microbial respiration for the carbon decomposition in each pool. The actual decomposition rate of carbon in each soil pool is calculated by

$$ K_{\text{ai}} = \left\{ {\begin{array}{*{20}c} {K_{i} L_{\text{C}} F, \, i = 1,2} \hfill \\ {K_{i} T_{\text{m}} F, \, i = 3} \hfill \\ {K_{i} F, \, i = 4,5,6,7,8} \hfill \\ \end{array} } \right., $$

(A29)

where i = 1, 2, 3, 4, 5, 6, 7, 8 represents the surface and soil structural materials, soil microbes, surface microbes, surface and soil metabolic material, slow and passive soil organic matter, respectively; K _i (day⁻¹) is the maximum decomposition rate. F is the response function of the decomposition rate to soil moisture and soil temperature:

$$ F = f(T)f(w_{\text{s}} ) $$

(A30)

$$ f(w_{s} ) = 0.8M_{sat}^{{\left( {\frac{{w_{s}^{b} - W_{opt}^{b} }}{{W_{opt}^{b} - 100^{b} }}} \right)^{2} }} + 0.2, $$

(A31)

where M _sat and b are soil-specific parameters, w _s is soil moisture (percentage of saturation W _sat), and W _opt is the optimal soil moisture for decomposition (percentage of saturation W _sat).

L _C is the impact of the lignin content of the structural material (L, g g⁻¹) on structural decomposition:

$$ L_{\text{C}} = {\text{e}}^{ - 3L}. $$

(A32)

T _m is the effect of soil texture on the turnover of soil microbes:

$$ T_{\text{m}} = 1 - 0.75(T_{\text{silt}} + T_{\text{clay}} ), $$

(A33)

where T _silt (%) and T _clay (%) are the silt and clay fractions, respectively.

Plant residues are divided into structural and metabolic materials according to the initial ratio of residue lignin (L) to nitrogen (N, g g⁻¹):

$$ F_{\text{m}} = 0.99 - 0.018\frac{L}{N}. $$

(A34)

Carbon leaves the soil microbe pool in four different flows: microbial respiration (F ₃), leaching of solute organic carbon (C _AL), and transfers to slow (C _AS) and passive (C _AP) soil organic matter. The fractions of carbon leaving the soil microbe pool due to the four different flows are calculated as

$$ C_{\text{AL}} = (0.2/18)(0.01 + 0.04T_{\text{sand}} ) $$

(A35)

$$ C_{\text{AP}} = 0.003 + 0.032T_{\text{clay}} $$

(A36)

$$ F_{3} = 0.85 - 0.68(T_{\text{silt}} + T_{\text{clay}} ) $$

(A37)

$$ C_{\text{AS}} = 1 - C_{\text{AL}} - C_{\text{AP}} - F_{3}. $$

(A38)

Net ecosystem exchange

Net ecosystem exchange is defined as the difference between GPP and respiration:

$$ {\text{NEE}} = {\text{GPP}} - {\text{RE}} = {\text{GPP}} - R_{\text{a}} - R_{\text{h}}. $$

(A39)

If there is no disturbance, NEE (g C m⁻²) can be considered the net carbon exchange between terrestrial ecosystems and the atmosphere.