Heterotrophic Respiration

In the DALEC heterotrophic respiration module, CO2 is respired both anaerobically and aerobically, while CH4 is only respired anaerobically. For each necromass pool (\(SClit\), \(SCcwd\), and \(SCsom\)), aerobic (\(FCrhaelit\), \(FCrhaecwd\), \(FCrhaesom\)) and anaerobic respiration (\(FCrhanlit\), \(FCrhancwd\), \(FCrhansom\)) are calculated as:

\[FCrhaelit(t) = SClit(t) Plit f_{V_{ae}}(t)f_{T}(t)f_{W}(t)(1- Plitxsom)\]
\[FCrhaecwd(t) = SClit(t) Pcwd f_{V_{ae}}(t)f_{T}(t)f_{W}(t)(1- Pcwdxsom)\]
\[FCrhaesom(t) = SCsom(t) Psom f_{V_{ae}}(t)f_{T}(t)f_{W}(t)\]
\[FCrhanlit(t) = SClit(t) Plit (1 - f_{V_{ae}}(t))f_{T}(t)Pfwc (1- Plitxsom)\]
\[FCrhancwd(t) = SClit(t) Pcwd (1 - f_{V_{ae}}(t))f_{T}(t)Pfwc (1- Pcwdxsom)\]
\[FCrhansom(t) = SCsom(t) Psom (1 - f_{V_{ae}}(t))f_{T}(t)Pfwc\]

where \(Plit\), \(Pcwd\), and \(Psom\) are the basal turnover rates of \(SClit\), \(SCcwd\), and \(SCsom\) respectively.

\(f_{V_{ae}}\) is the aerobic fraction of respiration, calculated as:

\[f_{V_{ae}} = (1 - \SMa)^{\PSfv}\]

where \(\SMa\) is the fractional soil moisture in layer 1, and \(\PSfv\) is an optimized regression scalar that determines the shape of the soil moisture response curve.

\(f_{Wc}\) is the soil moisture scalar when the soil is saturated; The anaerobic soil is saturated and thus \(f_{Wc}\) is given a constant value of 1 in equation (2); \(f_{V_{ae}}\) is the aerobic fraction of the vertical soil column; \(1 - f_{V_{ae}}\) is the anaerobic fraction of the soil. Equations (4) to (6) describe how \(f_{W}\) and \(f_{V_{ae}}\) are calculated.

DALEC resolves site-specific data-constrained parameters to characterize the shape of the soil moisture-respiration curve, where the soil moisture scalar (\(f_{W}\)) for aerobic respiration is based on the moisture of the aerobic soil (\(\theta_{ae}\)). By definition, the fractional soil moisture in layer 1 (\(\SMa\)) equals:

\[\SMa = \theta_{ae}f_{V_{ae}} + \theta_{an}(1 - f_{V_{ae}})\]

where \(\theta_{an}\) is the moisture of the anaerobic soil, which always equals 1; the volumetric fraction of anaerobic soil is (\(1 - f_{V_{ae}}\)); \(\theta_{ae}\) is then derived using the last two equations:

\[\theta_{ae} = ((\SMa-1)/f_{V_{ae}} +1)\]

According to Exbrayat et al. (2013), we use a segmented function to allow \(f_{W}\) to reach 1 at optimum soil moisture (\(\theta_{s_{opt}}\)), and then decrease to \(f_{W_{c}}\) (\(f_{W_{c}} \leq 1\)) to represent the high soil moisture suppression on aerobic respiration. Both \(\theta_{s_{opt}}\) and \(f_{W_{c}}\) are set to be optimized by the data.

\[\text{(placeholder for segmented function)}\]

\(f_T\) is a temperature scaling factor, defined as:

\[f_T(t) = \PQtenrhcotwo^{\frac{\STa(t) - 25^\circ\mathrm{C}}{10}}\]

where \(\PQtenrhcotwo\) is the factor by which respiration rate increases with a 10°C increase in temperature (relative to a reference temperature of 25°C) and \(\STa\) is the temperature of soil layer 1.

The heterotrophic respiration terms in the form of ({CO}_{2}) (({Rh}_{CO_{2}})) and ({CH}_{4}) (({Rh}_{CH_{4}})) are then calculated as:

\[{Rh}_{CO_{2}} = {Rh}_{ae}*1 + {Rh}_{an}*\left( 1 - f_{CH_{4}} \right)\]
\[{Rh}_{CH_{4}} = {Rh}_{ae}*0 + {Rh}_{an}*f_{CH_{4}}\]

where \(f_{CH_{4}}\) is the fraction of ({CH}_{4}) in anaerobic respiration:

\[f_{CH_{4}} = r_{CH_{4}}*Q_{10_{CH_{4}}}^{\frac{T - T_{mean}}{10}}\]

where \(r_{CH_{4}}\) is the potential ratio of anaerobically mineralized C released as CH4; \(Q_{10_{CH_{4}}}\) is the factor by which ({CH}_{4}) production rate increases with a 10°C increase in temperature, on top of the temperature sensitivity encountered in equations 1 and 2 (\(f_T\)). The reason we put a \(Q_{10_{CH_{4}}}\) on top of the general respiration temperature sensitivity term here is that studies have found higher temperature sensitivity in methane production than CO2 respiration across microbial to ecosystem scales (Yvon-Durocher et al. 2014). T is the mean air temperature of the current time step, \(T_{mean}\) is the multi-year mean air temperature at the region.