A new approach to estimate fine root production, mortality, and decomposition using litter bag experiments and soil core techniques

Abstract

Aims

A new approach is proposed to estimate fine root production, mortality, and decomposition that occur simultaneously in terrestrial ecosystems utilizing sequential soil core sampling or ingrowth core techniques.

Methods

The calculation assumes knowledge of the decomposition rate of dead fine roots during a given time period from a litter bag experiment. A mass balance model of organic matter derived from live fine roots is applied with an assumption about fine root mortality and decomposition to estimate decomposed dead fine roots from variables that can be quantified.

Results

Comparison of the estimated fine root dynamics with the decision matrix method and three new methods (forward estimate, continuous inflow estimate, and backward estimate) in a ca. 80-year-old Chamaecyparis obtusa plantation in central Japan showed that the decision matrix nearly always underestimated production, mortality, and decomposition by underscoring the values of the forward estimate, which theoretically underestimates the true value. The fine root production and mortality obtained by the decision matrix were on average 14% and 38% lower than those calculated by the continuous inflow estimate method. In addition, the values by the continuous inflow estimate method were always between those calculated by the forward estimate and backward estimate methods. The latter is known to overestimate the true value.

Conclusions

Therefore, we consider that the continuous inflow estimate method provides the best estimates of fine root production, mortality, and decomposition among the four approaches compared.

Appendix

Continuous inflow estimate of d _ij (Eq. 4 ): First, let us consider the decomposition process of dead fine roots occurring in a root litter bag treated with the ‘root-impermeable water-permeable (RIWP) sheet’ (see Materials and methods). The amount N of dead fine root is assumed to decompose with instantaneous decomposition of γ · N where γ is the decomposition rate. This process can be described by a differential equation, $dN/dt = - \gamma \cdot N$. With a boundary condition, $N = {N^C}_i$ at t = i, this differential equation is solved as

$$ N = {N^C}_i \cdot {e^{{ - \gamma \cdot (t - i)}}} $$

(A1)

If $N = {N^C}_j$ at t = j, and $\Delta t = j - i$, Equation A1 gives, ${N^C}_j = {N^C}_i \cdot {e^{{ - \gamma \cdot \Delta t}}}$. This relationship and Eq. 3 in the text yield an expression for the decomposition ratio of fine root necromass between times i and j, γ _ij , as

$$ {\gamma_{{ij}}} = 1 - {e^{{ - \gamma \cdot \Delta t}}} $$

(A2)

Note that γ and γ _ij in Eq. A2 are different parameters.

Next, let us consider the decomposition process of dead fine roots in an ingrowth core where there is both instantaneous fine root decomposition of γ N and instantaneous fine root mortality (addition of new dead roots) at a constant level of σ. Here, the process can be described by a differential equation:

$$ dN/dt = \sigma - \gamma \cdot N $$

(A3)

It is well known that the linear first-order differential equation of a form dy/dx + P(x)·y = Q(x) with two variables x and y has a solution (Kreyszig 1972):

$$ y = e^{{ - {\int {P{\left( x \right)}} }dx}} \cdot {\left\{ {{\int\limits_0^x {Q{\left( x \right)}e^{{{\int {P{\left( x \right)}dx} }}} } }dx + C} \right\}} $$

(A4)

where C is any constant. Therefore, Eq. A3 can be solved with a boundary condition, N = N _i at t = i, as,

$$ N = (\sigma /\gamma ) + ({N_i} - \sigma /\gamma ){e^{{ - \gamma \cdot (t - i)}}} $$

(A5)

By calculating N _j with Eq. A5 for t = j, then inserting Eq. A2, we obtain the relationship, $\sigma /\gamma = \Delta N/{\gamma_{{ij}}} + {N_i}$, where $\Delta N = {N_j} - {N_i}$. Applying this relationship in Eq. A5 yields,

$$ N = \Delta N \cdot (1 - {e^{{ - \gamma \cdot (t - i)}}})/{\gamma_{{ij}}} + {N_i} $$

(A6)

Then, by noting $\gamma \cdot \Delta t = - \ln (1 - {\gamma_{{ij}}})$ from Eq. A2, the amount of decomposed dead fine roots between times i and j could be obtained from Eq. A6 as,

$$ {d_{ij}} = {\text{ }}\int\limits_i^j {\gamma \cdot Ndt = - \Delta N - \left( {\Delta N/{\gamma _{ij}} + {N_i}} \right) \cdot \ln \left( {1 - {\gamma _{ij}}} \right)} $$

(A7)