A Microbial‐Explicit Soil Organic Carbon Decomposition Model (MESDM): Development and Testing at a Semiarid Grassland Site

Abstract

Explicit representations of microbial processes in soil organic carbon (SOC) decomposition models have received increasing attention, because soil heterotrophic respiration remains one of the greatest uncertainties in climate‐carbon feedbacks projected by Earth system models (ESMs). Microbial‐explicit models have been developed and applied in site‐ and global‐scale studies. These models, however, lack the ability to represent microbial respiration responses to drying‐wetting cycles, and few of them have been incorporated in land surface models (LSMs) and validated against field observations. In this study, we developed a multi‐layer, microbial‐explicit soil organic carbon decomposition model (MESDM), based on two main assumptions that (a) extracellular enzymes remain active at dry reaction microsites, and (b) microbes at wet microsites are active or potentially active, while microbes at the dry microsites are dormant, by dividing the soil volume into wet and dry zones. MESDM with O₂ and CO₂ gas transport models was coupled with Noah‐MP LSM and tested against half‐hourly field observations at a semiarid grassland site in the southwest US characterized by pulsed precipitation. The results show MESDM can reproduce the observed soil respiration pulses of various sizes in response to discrete precipitation events (Birch effect) and thus improve the simulation of net ecosystem exchange. Here, both microbial accessibility to accumulated dissolved organic carbon and reactivation of dormant microbes at the dry microsites upon rewetting are critical to reproducing the Birch effect. This study improves our understanding of and ability to simulate complex soil carbon dynamics that experience drying‐wetting cycle in climate‐carbon feedbacks.

Introduction

Soil is the largest pool of terrestrial organic carbon (C), storing more than 2,300 Pg C (1 Pg = 1 × 10¹⁵ g), which is nearly four times the amount of C stored in plant biomass (Jobbágy & Jackson, 2000; Schlesinger & Bernhardt, 2013) and three times the amount of C in the atmosphere (Schmidt et al., 2011). As one of the primary paths through which CO₂ fixed by plants returns to the atmosphere, microbial decomposition of soil organic carbon (SOC) is one of the most important processes in the global carbon cycle and is expected to accelerate in response to climate warming, causing a carbon cycle-climate feedback (Arora et al., 2020; Bardgett et al., 2008). However, a number of studies in the fifth and sixth phases of the Coupled Model Intercomparison Project (CMIP) have shown that the representation of soil heterotrophic respiration processes in Earth system models (ESMs) remains one of the greatest uncertainties in predicting climate-carbon feedbacks (Arora et al., 2013, 2020; Bailey et al., 2018; Friedlingstein et al., 2014; Todd-Brown et al., 2013). Therefore, a better understanding of soil heterotrophic respiration processes would help improve projections of this feedback effect.

Most land models in ESMs describe microbial SOC decomposition with the first-order kinetics. In these models, the CO₂ production rate of each substrate pool is proportional to the size of the pool with the different turnover rate according to substrate recalcitrance (substrate concentration and quality) and modified by empirical functions of temperature (constant Q₁₀ or Arrhenius relationship) and water content. Different empirical functions of temperature and water content in the CMIP models may be the major source of uncertainty in the projected soil heterotrophic respiration at global scale (Todd-Brown et al., 2012). Moreover, the conventional first-order decay models fail to reproduce the soil respiration pulses in response to soil drying-wetting cycles (known as “Birch effect”; Birch, 1958). The Birch effect may exert a remarkable influence on the soil carbon dynamics in arid and semiarid ecosystems with episodic water availability (Austin et al., 2004; Huxman et al., 2004; Manzoni et al., 2020). Representations of SOC decomposition in the CIMP ESMs have lagged behind our current understanding of microbial decomposition mechanisms (Arora et al., 2020; Todd-Brown et al., 2012, 2013).

A large number of studies have revealed that microbes play critical roles in the global carbon cycle by controlling SOC decomposition (Bardgett et al., 2008; Conrad, 1996; Schimel & Schaeffer, 2012; Zhou et al., 2012). Microbes produce extracellular enzymes (EE) to degrade complex SOC into dissolved organic carbon (DOC) through catalysis, take up DOC, convert the assimilated C into microbial biomass for growth, and release CO₂ through respiration (Schimel & Weintraub, 2003). As the two most important environmental variables (Moyano et al., 2013; Parton et al., 1987; Raich & Schlesinger, 1992), temperature and moisture may have direct and indirect impacts on microbial and enzymatic activities and thus affect the rate of SOC decomposition in a complex way (Davidson & Janssens, 2006). In addition, it is well recognized that oxygen availability limits the microbial activity when the soil water approaches saturation (Davidson et al., 2012; Skopp et al., 1990). Furthermore, in response to alterations in the environmental conditions, microbial communities may change in biomass, shift in composition, change in physiological state, adapt physiologically (Allison & Treseder, 2010; Castro et al., 2010; Schimel et al., 1999; S. E. Evans & Wallenstein, 2012) and thus are expected to mediate decomposition response to climate change (Bardgett et al., 2008; Bradford et al., 2010; Luo et al., 2001; Todd-Brown et al., 2012). Therefore, it is critical for mechanistically understanding of the response of microbial processes to environmental changes for investigating the carbon-climate feedbacks. Explicitly representing the soil microbial processes in land surface models (LSMs) as one of the important components of ESMs would improve our ability to generate a realistic simulation of soil heterotrophic respiration responses to environmental changes (Todd-Brown et al., 2012; Wieder et al., 2015).

In recent decades, a great number of microbial-explicit models have been developed to represent the effects of microbial processes on SOC decomposition based on advances in the understanding of microbial decomposition (e.g., Abramoff et al., 2017; Allison et al., 2010; Davidson et al., 2012; He et al., 2015; He et al., 2021; Huang et al., 2018; Kaiser et al., 2014; Lawrence et al., 2009; Liu et al., 2019; Manzoni et al., 2014, 2016; Moorhead & Sinsabaugh, 2006; Moyano et al., 2018; Schimel & Weintraub, 2003; Sulman et al., 2014; Tang & Riley, 2015; Wang et al., 2015; Wieder et al., 2013, 2014). In these models, the temperature sensitivities of the enzyme-catalyzed degradation of SOC into DOC and microbial uptake are described according to the Arrhenius kinetics, while the limitations of substrate and enzyme concentrations or microbial biomass on the degradation and uptake rates are represented using the Michaelis-Menten kinetics. Moreover, temperature may affect the microbial carbon use efficiency (CUE) and thus change microbial biomass, enzyme production, and microbial respiration (Frey et al., 2013). However, there is a major discrepancy among the microbial-enzyme models in representing the effect of soil moisture on SOC degradation and DOC uptake rates. Some models use empirical functions of soil moisture content to meditate the decomposition rate (He et al., 2015; Huang et al., 2018; Lawrence et al., 2009; Wang et al., 2019;), while others describe moisture-regulated diffusion constraints on substrate and enzyme availabilities (Abramoff et al., 2017; Davidson et al., 2012; Kaiser et al., 2014; Moyano et al., 2018). In a few models, the influence of O₂ availability on the microbial uptake rate is taken into account using the Michaelis-Menten kinetics (Abramoff et al., 2017; Davidson et al., 2012; Sulman et al., 2014; Zhang et al., 2014). Many microbial-explicit models have shown a better capability of simulating soil respirations at lab and field scales and SOC stock dynamics at global scales than conventional first-order decay models. Moreover, a few models are able to simulate the Birch effect observed in laboratory (Evans et al., 2016; Lawrence et al., 2009; Liu et al., 2019) and field experiments (Zhang et al., 2014), or in numerical experiment (Manzoni et al., 2014), by implementing the mechanism of accumulated DOC in dry soil becoming bioavailable upon wetting. However, these models, being tested under static-temperature conditions, are difficult to incorporate into LSMs due to the use of empirical functions of soil moisture and the lack of validation against field observations (Evans et al., 2016; Lawrence et al., 2009; Liu et al., 2019; Manzoni et al., 2014). Furthermore, microbial model intercomparisons have shown that a larger disagreement in the modeled global soil carbon dynamics mainly results from moisture rather than temperature responses (Wieder et al., 2018). Therefore, it is still challenging to improve the parameterizations of the soil respiration responses to soil moisture, especially to the drying-rewetting cycles, in microbial-explicit models and to predict a more realistic Birch effect at field scales.

Among recently microbial-explicit models, some models consider microbial physiological state changes when simulating SOC dynamics (Evans et al., 2016; He et al., 2015; Huang et al., 2018; Liu et al., 2019; Manzoni et al., 2014; Salazar et al., 2018; Tang & Riley, 2015; Wang et al., 2015). A large number of studies have shown that less than 5% of live microbes are in a metabolically active state in the absence of easily available substrates (Anderson & Domsch, 1985; Blagodatskaya & Kuzyakov, 2013; Lennon & Jones, 2011). Under unfavorable environmental conditions, soil microbes enter a dormant state of low to zero metabolic activity to alleviate loss of biomass (Stolpovsky et al., 2011). Only the active fraction of a microbial community can assimilate DOC taken up from a soil solution for maintenance and growth respirations, enzyme synthesis, new cell production, and so on (Blagodatskaya & Kuzyakov, 2013). Thus, for survival, the dormant microbes consume their biomass to sustain a maintenance respiration rate that is about two to three orders of magnitude lower than that of metabolically active microbes (Anderson & Domsch, 1985; Lennon & Jones, 2011). There is a reversible transition between active and dormant microbes that may occur in response to changes in environmental conditions (Skopp et al., 1990; Van De Werf & Verstraete, 1987). A potentially active soil microbe state is considered to exist in the soil between the active and dormant states, and there is a rapid switch from a potentially active to an active state in minutes to hours, while the transition from a dormant to an active state occurs over hours to days (Blagodatskaya & Kuzyakov, 2013). The existing microbial-explicit models considering microbial dormancy represent the simultaneous dormancy and reactivation rates (He et al., 2015; Huang et al., 2018; Manzoni et al., 2014; Wang et al., 2015), or the fraction of active microbial biomass (Salazar et al., 2018), or microbial functional groups including producers (producing EE) and cheaters (not producing EE) (Evans et al., 2016). In these models, the changes of active and dormant microbial biomass are assumed to eventually depend on substrate concentrations and reaction rates (including growth and maintenance respirations) that are modified through different empirical functions of soil moisture content or soil matric water potential.

Activation of dormant microbes upon wetting of dry soils may be one of the mechanisms responsible for the Birch effect, because the amount of active microbial biomass in soils determine microbial respiration rate (Blagodatskaya & Kuzyakov, 2013) and wetting-induced activation of dormant microorganisms helps explain the soil CO₂ pulses observed in both laboratory incubation and field experiments (Placella et al., 2012; Salazar-Villegas et al., 2016; Stolpovsky et al., 2011). Recent model studies have shown that accounting for microbial dormancy in microbial-explicit models can help reproduce the Birch effect (Evans et al., 2016; Liu et al., 2019) and improve predictions of microbial respiration under warming and drying-wetting cycles in laboratory experiments (Salazar et al., 2018). Additionally, activation of dormant microbes was considered to be one of the main mechanisms that microbial-explicit models can adopt to capture the observed priming effect in incubation experiments (Huang et al., 2018). However, parameterizations of microbial physiological state changes in current models have been based on empirical functions without a mechanistic representation or consideration of soil microbes at the potentially active state. Moreover, few models considering microbial dormancy have been used to simulate the Birch effect observed in field experiments.

Microbial-explicit models have been increasingly used in both site- and global-scale studies from hourly to daily timescales. Most microbial-explicit models represent the soil as a bulk layer without specification of vertical distributions of SOC in the profile. However, the vertical distribution of SOC obviously affects the soil carbon dynamics (Braakhekke et al., 2011; Dwivedi et al., 2017; Koven et al., 2013). Soil temperature and moisture show large vertical gradients and undergo marked short-term variations caused by sporadic precipitation, especially at the upper soil layers. Additionally, the vertical distribution of roots regulates the profiles of root litter and exudate input (Walker et al., 2003). Thus, explicitly resolving the vertical profiles of various C pools, temperature, moisture contents, and O₂ concentrations as well as root litter and exudate inputs in microbial-explicit models should better represent the profile of heterotrophic respiration rate (Ahrens et al., 2015; Braakhekke et al., 2011; Wieder et al., 2018). Because the transition of microbial metabolic activities from a dormant state to an active state in response to substrate addition and rapid environmental change may occur within a few hours (Blagodatskaya & Kuzyakov, 2013; Placella et al., 2012), an hourly temporal resolution can help capture the rapid variations in soil respiration (Davidson et al., 2012; Wieder et al., 2018). Currently, a few microbial-explicit models with one to two soil layers have been incorporated in LSMs and improved global-scale SOC stock projections (Wang et al., 2017; Wieder et al., 2013). Only two models integrated into a LSM at a high soil vertical resolution have reproduced the observed ecosystem-scale SOC pattern under elevated CO₂ (Sulman et al., 2014) or simulated the fungal and bacterial biomass at the site level (He et al., 2021). However, few models with high soil vertical resolutions and hourly time steps have been incorporated into LSMs and rigorously validated against hourly field observations.

In this study, we developed a microbial-explicit soil organic carbon decomposition model (MESDM) with a high vertical resolution and half-hourly time step, incorporated it into the Noah-MP LSM in place of the original first-order decay model (Niu et al., 2011), and tested the coupled model against field measurements. As opposed to other models, MESDM divides the soil volume of each soil layer into wet and dry zones and represents two major processes: (a) soil moisture controls on enzyme-catalyzed SOC depolymerization to DOC and microbial uptake of DOC, and (b) soil moisture controls on microbial physiological state and its transformation considering the effect of substrate availability and temperature. We further coupled the multi-layer MESDM with O₂ and CO₂ gas vertical transport models to calculate the O₂ and CO₂ concentrations at various depths and the CO₂ effluxes at the soil surface. We tested the coupled model from hourly to seasonal scales against the observed soil CO₂ concentration at various depths and net ecosystem exchange (NEE) as well as the soil CO₂ efflux at the Santa Rita site in a semiarid grassland in the southwest US, which is characterized by pulsed precipitation and high temperature.

Materials and Methods MESDM Description

MESDM represents four types of carbon pools including polymeric SOC, DOC, microbial biomass carbon (MBC), and extracellular enzyme pool (ENZ) following the models of Schimel and Weintraub (2003) and Allison et al. (2010) (Figure 1). It represents three major processes including: (a) microbial depolymerization of SOC into DOC through extracellular enzymatic catalysis; (b) microbial uptake of DOC limited by O₂ concentration; and (c) microbial assimilation of DOC into maintenance respiration, production (cells or enzyme) and its required respiration.

Figure 1. Schematic diagram of microbial-explicit soil organic carbon decomposition model representing the processes of microbial depolymerization of soil organic carbon (SOC) into dissolved organic carbon (DOC) through catalysis of extracellular enzyme pool (ENZ) produced by microbe pool (MBC), microbial uptake of DOC, and respiration. Blue and red boxes denote the wet and dry zones of the soil volume. Solid lines with two-way arrows denote the transitions of DOCs, ENZs, and MBCs between the wet and dry zones.

MESDM divides the soil volume of each layer with homogeneous soil matrix into dry and wet zones according to soil water content (Zhang et al., 2014). We assume that the soil matrix is surrounded by water film in the wet zone and is exposed to soil pore air in the dry zone. For simplicity, we consider the volume fraction of the wet zone to be equal to the relative water saturation, $$w$$, and that of the dry zone to be equal to the remaining fraction, $$(1\mbox{-}w)$$ ($$w={\theta }_{l}/{\theta }_{s}$$, where $${\theta }_{l}$$ and $${\theta }_{s}$$ are the volumetric soil liquid water content and porosity [m³ m⁻³], respectively). The DOC, MBC, and ENZ pools in the bulk soil are separated into two sub-pools, one in the wet zone and the other in the dry zone (hereafter, the DOC pools in the wet and dry zones are called wet and dry DOCs, respectively, and so for MBC and ENZ; Figure 1). In such a way, MESDM accounts for spatially heterogeneous distributions of carbon pools and biochemical reaction rates at the microsite scales as a result of the spatial distributions of soil water in the soil pores (Wanzek et al., 2018). Hereafter, the microsites of the soil pores in the wet and dry zones are called dry and wet microsites, respectively.

Because EE may remain active at the dry microsites (Parker & Schimel, 2011; Stursova & Sinsabaugh, 2008), MESDM assumes that the dry DOC can be produced through enzyme catalysis and thus accumulate due to its inaccessibility by microbes due to the absence of water in the dry zone (Figure 1). However, enzyme immobilization at the dry microsites may lead to a reduced enzyme efficiency (approximately 40% of that at the wet microsites), explaining the potential (rather than actual) enzyme activity (Alster et al., 2013; Nannipieri et al., 2002, 2018). Also, enzymes have lower turnover rates in the dry zone than in the soil solution due to protection from degradation (Nannipieri et al., 2002; Steinweg et al., 2012, 2013).

MESDM assumes that microbes at the wet microsites, living in a soil solution, are in metabolically active or potentially active states due to, while microbes at the dry microsites are in dormancy; thus, changes in soil water content can alter the physiological state of a portion of the microbes. Only at the wet microsites can active microbes take up DOC through cell membrane transport, because all microbial uptake functions require a water environment (Marschner & Kalbitz, 2003; Figure 1). The active microbes may assimilate all DOCs taken up. Since EE is a prerequisite for the success of soil active microbes, EE production is the first priority in the utilization of the assimilated DOC over satisfying the requirements for microbial maintenance respiration, and the remaining fraction is allocated to active microbial growth and growth respiration (Schimel & Weintraub, 2003). About 1%–5% of DOC taken up by active microbes is preferentially allocated to EE production (Burns et al., 2013; Schimel & Weintraub, 2003).

MESDM assumes that when the excess of assimilated DOC over EE production and associated supportive respiration are not able to meet the demand for maintenance respiration but sustain over a half of the demand, all active microbes will stop growing and remain a normal state of maintenance respiration, consuming their own biomass (Blagodatskaya & Kuzyakov, 2013). This may occur under unfavorable conditions due to the stress of low substrate availability, resulting in a starvation state of the active microbes. If starvation worsens, all active microbes at the wet microsites enter a potentially active state within minutes to hours. In addition, extreme thermal stresses, that is, either too high (>45°C) or too low temperatures (<0°C), may force the active microbes into the potentially active state or death. MESDM also represents that (a) the potentially active microbes at the wet microsites stop DOC uptake and EE production and are rapidly reactivated in response to substrate additions (e.g., plant litter and exudate inputs, and O₂ supply) or environmental changes (e.g., warming and cooling) within a few hours (Blagodatskaya & Kuzyakov, 2013) and (b) they require energy for maintenance by consuming their biomass at a much low metabolic rate that is the same as that of dormant microbes. While the dormant microbes never die (Wang et al., 2015), the death rate of the potentially active microbes is assumed to be one order of magnitude lower than that of active microbes.

When the soil water saturation at a layer is altered, variations in the volumes of the wet and dry zones will accordingly lead to changes in the sizes of the corresponding DOC, ENZ, and MBC pools (Figure 1). Thus, on the basis of mass conservation, transitions of DOC and ENZ between wet and dry zones are assumed to occur, as are transformations between dormant and active or potentially active MBCs. Both SOC in the dry and wet zones can be depolymerized by EE. But for simplification, we calculate the bulk SOC pool in each soil layer without considering SOC sub-pools because the SOC concentration is approximately two orders of magnitude larger than the depolymerization rate of SOC on the annual scale. The mass balance equations of the carbon pools and formulations of the transition rates of DOC, MBC, and ENZ between wet and dry zones are given as follows (see also Table 1 for the variables and parameters).

Table 1 Model Variables and Parameters Used in MESDM

	Description	Unit
Variable
$${C}_{\text{SOC}}$$	SOC concentration per unit volume of bulk soil	g C m−3
$${C}_{\text{DOC}}$$	DOC concentration per unit volume of bulk soil
$${C}_{\text{DOC}\_\text{W}}$$	DOC concentration at the reaction microsite in the wet zone	g C m−3
$${C}_{\text{DOC}\_\text{D}}$$	DOC concentration at the reaction microsite in the dry zone	g C m−3
$${C}_{\text{MBC}}$$	MBC concentration per unit volume of bulk soil
$${C}_{\text{MBC}\_\text{WA}}$$	Active MBC concentration at the reaction microsite in the wet zone	g C m−3
$${C}_{\text{MBC}\_\text{WP}}$$	Potentially active MBC concentration at the reaction microsite in the wet zone	g C m−3
$${C}_{\text{MBC}\_\text{D}}$$	Dormant MBC concentration at the reaction microsite in the dry zone	g C m−3
$${C}_{\text{ENZ}}$$	ENZ concentration per unit volume of bulk soil
$${C}_{\text{ENZ}\_\text{W}}$$	ENZ concentration at the reaction microsite in the wet zone	g C m−3
$${C}_{\text{ENZ}\_\text{D}}$$	ENZ concentration at the reaction microsite in the dry zone	g C m−3
$${C}_{{\mathrm{O}}_{2}}$$	O2 concentration in soil pore air	m3 O2 m−3 air
$${C}_{\text{litter}}$$	Input rate of litter C to the soil C pool	g C m−3 s−1
$${K}_{m}$$	Half-saturation constant for SOC as a linear function of temperature	g C m−3
$${K}_{\text{m}\_\text{updoc}}$$	Half-saturation constant for DOC	g C m−3
$${R}_{\text{Am}}$$	Active microbial maintenance respiration rate	g C m−3 s−1
$${R}_{\text{Dm}}$$	Dormant microbial maintenance respiration rate	g C m−3 s−1
$${R}_{e}$$	Respiration rate necessary to support EE production	g C m−3 s−1
$${R}_{g}$$	Growth respiration rate of active microbes	g C m−3 s−1
$${R}_{h}$$	Microbial heterotrophic respiration rate	g C m−3 s−1
$${S}_{\text{DOC}}$$	DOC transition rate between dry and wet zones due to changes in soil water content per unit volume of bulk soil	g C m−3 s−1
$${S}_{\text{ENZ}}$$	ENZ transition rate between dry and wet zones due to changes in soil water content per unit volume of bulk soil	g C m−3 s−1
$${S}_{\text{MBC}}$$	MBC transformation rate between dry and wet zones due to water content changes per unit volume of bulk soil	g C m−3 s−1
$$t$$	Time	s
$$T$$	Soil temperature in kelvin	K
$${V}_{\text{EXD}}$$	Root exudate input rate per unit volume of bulk soil	g C m−3 s−1
$${V}_{\text{DOC}}$$	Active microbial assimilation rate of DOC at the reaction microsite in the wet zones	g C m−3 s−1
$${V}_{\mathrm{max}}$$	Maximum potential SOC depolymerization rate per unit ENZ when substrate concentration is not limiting	g C m−3 (g C m−3)−1 s−1
$${V}_{\text{max}\_\text{up}}$$	Maximum potential DOC uptake rate per unit MBC when substrate concentrations are not limiting	g C m−3 (g C m−3)−1 s−1
$${V}_{\text{SOC}}$$	Depolymerization rate of SOC to DOC	g C m−3 s−1
$${V}_{\text{SOC}\_\text{W}}$$	Depolymerization rates of SOC to DOC in the wet zone	g C m−3 s−1
$${V}_{\text{SOC}\_\text{D}}$$	Depolymerization rates of SOC to DOC in the dry zone	g C m−3 s−1
$$w$$	Relative water saturation
$$\varepsilon $$	Carbon use efficiency
$${\theta }_{l}$$	Volumetric soil water content	m3 m−3
$${\theta }_{s}$$	Soil porosity	m3 m−3
Parameter
$$b$$	A factor that reduces potentially active and dormant microbial maintenance respiration rates
$${E}_{a}$$	Activation energy for SOC depolymerization	J mol−1
$${E}_{\text{a}\_\text{up}}$$	Activation energy for DOC uptake	J mol−1
$${E}_{\text{a}\_\text{mr}}$$	Activation energy for maintenance respiration	J mol−1
$${k}_{e}$$	The fraction of DOC taken up that is allocated to EE production
$${K}_{m0}$$	Intercept of the half-saturation constant for SOC depolymerization as a linear function of temperature	g C m−3
$${K}_{\text{m0}\_\text{upDOC}}$$	Intercept of the half-saturation constant for DOC uptake as a linear function of temperature	g C m−3
$${K}_{{\text{m}\_\text{upO}}_{2}}$$	Half-saturation constant for O2	m3 O2 m−3 air
$${m}_{\varepsilon }$$	Slope of CUE as a linear function of temperature	°C−1
$${m}_{{K}_{m}}$$	Slope of the half-saturation constant for SOC depolymerization as a linear function of temperature	g C m−3 °C−1
$${m}_{{K}_{\text{m}\_\text{upDOC}}}$$	Slope of the half-saturation constant for DOC taken up as a linear function of temperature	g C m−3 °C−1
$${T}_{\text{ref}}$$	Reference temperature	K
$${V}_{\mathrm{max}0}$$	Maximum SOC depolymerization rate per unit ENZ at the reference temperature	g C m−3 (g C m−3)−1 s−1
$${V}_{\text{max0}\_\text{up}}$$	Maximum DOC uptake rate per unit MBC at the reference temperature	g C m−3 (g C m−3)−1 s−1
$${V}_{\text{0}\_\text{mr}}$$	Active microbial maintenance respiration rate per unit MBC at the reference temperature	g C m−3 (g C m−3)−1 s−1
$$\alpha $$	The fraction of litter allocated to SOC
$${\varepsilon }_{e}$$	Enzyme efficiency of catalysis in the dry zone
$${\varepsilon }_{0}$$	Intercept of carbon use efficiency (CUE) as a linear function of temperature
$$\sigma $$	The fraction of dead microbial biomass allocated to SOC
$$\eta $$	A factor that reduces enzyme turnover rate in the dry zone
$$\lambda $$	A factor that reduces the potential active microbe death rate
$${\tau }_{m}$$	Microbial biomass death rate constant	s−1
$${\tau }_{e}$$	Enzyme turnover rate constant in the wet zone	s−1

Note. EE, extracellular enzyme; ENZ, extracellular enzyme pool; MESDM, microbial-explicit soil organic carbon decomposition model; SOC, soil organic carbon; DOC, dissolved organic carbon; MBC, microbial biomass carbon.

SOC Pool

The SOC concentration, $${C}_{\text{SOC}}$$ (g C m⁻³), per unit volume of bulk soil decreases with depolymerization losses and increases due to external inputs, including a fraction of dead microbial biomass and a portion from litter: [Image Omitted. See PDF]where $$t$$ is the time (s), $${V}_{\text{SOC}}$$ is the depolymerization rate of SOC to DOC (g C m⁻³ s⁻¹), $${C}_{\text{MBC}\_\text{WA}}$$ and $${C}_{\text{MBC}\_\text{WP}}$$ are the active and potentially active MBC concentrations at the wet reaction microsites, respectively (g C m⁻³), $${\tau }_{m}$$ is the active microbe death rate constant (s⁻¹), $$\sigma $$ is the fraction of dead microbial biomass that enters SOC, $${C}_{\text{litter}}$$ is the input rate of litter C to the soil C pool (g C m⁻³ s⁻¹), and $$\alpha $$ is the fraction of litter that enters SOC. MESDM calculates microbial death rate as a first-order process with $${\tau }_{m}$$ for active microbes and $$\lambda \cdot {\tau }_{m}$$ ($$\lambda =0.1$$, a factor reducing death rate) for potentially active microbes, and the fraction of dead MBC is recognized as a source for the SOC pool (Allison et al., 2010).

DOCs may be produced in both wet and dry soil zones. According to the volume fractions of the wet and dry zones, the total depolymerization rate of SOC to DOC per unit volume of bulk soil is given as follows: [Image Omitted. See PDF]where $${V}_{\text{SOC}\_\text{W}}$$ and $${V}_{\text{SOC}\_\text{D}}$$ are the SOC depolymerization rates at the wet and dry reaction microsites, respectively (g C m⁻³ s⁻¹). $${V}_{\text{SOC}\_\text{W}}$$ and $${V}_{\text{SOC}\_\text{D}}$$ are the catalyzed reaction rates following Michaelis-Menten kinetics (Allison et al., 2010; Wang & Post, 2013), scaled to the ENZ concentrations at the wet and dry reaction microsites ($${C}_{\text{ENZ}\_\text{W}}$$ and $${C}_{\text{ENZ}\_\text{D}}$$, g C m⁻³), respectively: [Image Omitted. See PDF] [Image Omitted. See PDF]where $${V}_{\mathrm{max}}$$ is the maximum potential SOC depolymerization rate per unit ENZ (g C m⁻³ (g C m⁻³)⁻¹ s⁻¹) when the substrate concentration is not limiting, $${K}_{m}$$ is the half-saturation constant (g C m⁻³) for SOC, and $${\varepsilon }_{e}$$ is the enzyme efficiency of catalysis in the dry zone (=0.4 in this study), which is reduced due to immobilization of dry EE (Alster et al., 2013). $${V}_{\mathrm{max}}$$ is calculated according to the Arrhenius kinetics: [Image Omitted. See PDF]where $${V}_{\mathrm{max}0}$$ is the maximum SOC depolymerization rate per unit ENZ at the reference temperature $${T}_{\text{ref}}=283.15\hspace*{.5em}\mathrm{K}$$ (g C m⁻³ (g C m⁻³)⁻¹ s⁻¹), $${E}_{a}$$ is the activation energy of SOC depolymerization (J mol⁻¹), $$R$$ is the universal gas constant (=8.31 J mol⁻¹ K⁻¹), and $$T$$ is the soil temperature (K). Equation 5 shows a well-established temperature sensitivity provided that the substrate concentration is not limiting. $${K}_{m}$$ is represented as a linear function of temperature with a slope of $${m}_{{K}_{m}}$$ (g C m⁻³ °C⁻¹) and an intercept of $${K}_{m0}$$ (g C m⁻³): [Image Omitted. See PDF]

DOC Pool

The DOC concentration per unit volume of bulk soil, $${C}_{\text{DOC}}$$ (g C m⁻³), in each soil layer comprises the bulk wet and dry DOC concentrations: [Image Omitted. See PDF]where $${C}_{\text{DOC}\_\text{W}}$$ and $${C}_{\text{DOC}\_\text{D}}$$ are the DOC concentrations at the wet and dry reaction microsites, respectively (g C m⁻³).

The wet DOC pool per unit volume of bulk soil receives inputs from depolymerized SOC, deactivated wet enzymes, a fraction of litter, the remaining fraction of dead microbial biomass, root exudates, and DOC transitions between dry and wet zones due to variations in soil water content, while the wet DOC pool declines due to microbial assimilation of wet DOC: [Image Omitted. See PDF]where $${V}_{\text{DOC}}$$ is the active microbial assimilation rate of DOC at the wet microsites (g C m⁻³ s⁻¹), $${\tau }_{e}$$ is the enzyme turnover constant rate in the wet zone (s⁻¹), $${V}_{\text{EXD}}$$ is the root exudate rate per unit volume of bulk soil (g C m⁻³ s⁻¹), and $${S}_{\text{DOC}}$$ is the DOC transition rate between the dry and wet zones due to changes in soil water content per unit volume of bulk soil (g C m⁻³ s⁻¹). Enzyme turnover in the wet zone is modeled as a first-order decay process with $${\tau }_{e}$$, and deactivated EE in the wet zone is added into the wet DOC pool. We assume that DOC from litter enters the wet and dry DOC pools according to the volume fraction of the two zones and that all root exudates are released into the wet DOC pool due to the control of soil water on their release (Walker et al., 2003). When soil water content changes, $${S}_{\text{DOC}}$$ needs to be estimated as follows: [Image Omitted. See PDF]

The active microbial uptake rate at the wet microsites is a function of the concentrations of wet DOC and O₂ in soil air following Michaelis-Menten kinetics scaled to the size of the active MBC pool (Davidson et al., 2012): [Image Omitted. See PDF]where $${V}_{\text{max}\_\text{up}}$$ is the maximum potential DOC uptake rate per unit MBC (g C m⁻³ (g C m⁻³)⁻¹ s⁻¹) when substrate concentrations are not limiting, $${C}_{{\mathrm{O}}_{2}}$$ (m³ O₂ m⁻³ air) is the concentration of O₂ in soil pore air, and $${K}_{\text{m}\_\text{updoc}}$$ (g C m⁻³ soil) and $${K}_{{\text{m}\_\text{upO}}_{2}}$$ (m³ O₂ m⁻³ air) are the corresponding Michaelis-Menten constants for DOC and O₂, respectively. Microbes can take up dissolved O₂ in soil water for their respiratory requirements. The dissolved O₂ concentration in soil water is assumed to be in equilibrium with the O₂ concentration in the soil air where O₂ transport in gas is approximately 10⁴ times larger than that in soil liquid water. Thus, we directly use the O₂ concentration in the soil air to describe the effect of the dissolved O₂ concentration on the uptake rate (Fang & Moncrieff, 1999). When soil water content increases, the decreased O₂ concentration resulting from diffusion limitation tends to constrain microbial aerobic activities.

The temperature sensitivity of DOC uptake is described in the same way as SOC decomposition, and $${V}_{\text{max}\_\text{up}}$$ is calculated according to Arrhenius kinetics as follows: [Image Omitted. See PDF]where $${V}_{\text{max0}\_\text{up}}$$ is the maximum DOC uptake rate per unit MBC (g C m⁻³ (g C m⁻³)⁻¹ s⁻¹) at the reference temperature $${T}_{\text{ref}}$$ and $${E}_{\text{a}\_\text{up}}$$ is the activation energy of DOC uptake (J mol⁻¹). $${K}_{\text{m}\_\text{upDOC}}$$ is also assumed to be a linear function of temperature: [Image Omitted. See PDF]where $${m}_{{K}_{\text{m}\_\text{upDOC}}}$$ and $${K}_{\text{m0}\_\text{upDOC}}$$ are the slope (g C m⁻³ °C⁻¹) and intercept (g C m⁻³) factors, respectively. $${K}_{{\text{m}\_\text{upO}}_{2}}$$ is considered to be constant with respect to temperature due to a lack of data to support it as a function of temperature (Davidson et al., 2012).

The dry DOC pool per unit volume of bulk soil receives dry DOC fluxes from the depolymerized SOC, deactivated dry enzymes, a remaining portion of the DOC from litter that enters the dry zone and DOC transitions between dry and wet zones due to variations in soil water content: [Image Omitted. See PDF]where $$\eta $$ is a factor that reduces the enzyme turnover in the dry zone (=0.6 in this study). Deactivated EE in the dry zone enters the dry DOC pool.

MBC Pool

The MBC concentration per unit volume of bulk soil, $${C}_{\text{MBC}}$$ (g C m⁻³), comprises the bulk dormant and active or potentially active MBC concentrations: [Image Omitted. See PDF] [Image Omitted. See PDF]where $${C}_{\text{MBC}\_\text{D}}$$ is the dormant MBC concentration at the dry reaction microsites (g C m⁻³), $${k}_{e}$$ is the constant percentage of assimilated DOC by which enzymes are produced, $${R}_{e}$$ is the respiration rate necessary to support EE production at the wet microsites, and $${R}_{\text{Am}}$$ is the active microbial maintenance respiration rate at the wet microsites (g C m⁻³ s⁻¹). Microbial maintenance respiration is represented to be proportional to the microbial biomass regulated by temperature according to Arrhenius kinetics (Schimel & Weintraub, 2003). Thus, $${R}_{\text{Am}}$$ is calculated as: [Image Omitted. See PDF]where $${V}_{\text{0}\_\text{mr}}$$ is the active microbial maintenance respiration rate per unit MBC at the reference temperature (g C m⁻³ (g C m⁻³)⁻¹ s⁻¹) and $${E}_{\text{a}\_\text{mr}}$$ is the activation energy of active microbial maintenance respiration (J mol⁻¹).

The active MBC pool per unit volume of bulk soil increases via growth and decreases due to biomass death or the fraction of maintenance respiration while changing via MBC transformation between the dry and wet zones due to variations in soil water content: [Image Omitted. See PDF] [Image Omitted. See PDF]where $$\varepsilon $$ is the CUE parameter and $${S}_{\text{MBC}}$$ is the MBC transformation rate between active and dormant microbes due to water content changes (g C m⁻³ s⁻¹). The term $$({V}_{\text{DOC}}-{V}_{\text{DOC}}\cdot {k}_{e}-{R}_{e}-{R}_{\text{Am}})\cdot \varepsilon $$ in Equation 17 is the portion of assimilated DOC that is converted into biomass. Equation 18 represents the active microbes in a starvation state. $$\varepsilon $$ is also the EE production efficiency by which $${R}_{e}$$ is calculated: [Image Omitted. See PDF]

Some evidences show that $$\varepsilon $$ declines with increasing temperature. $$\varepsilon $$ is thus described as a linear function of temperature with a slope parameter $${m}_{\varepsilon }$$ (℃⁻¹) and an intercept $${\varepsilon }_{0}$$: [Image Omitted. See PDF]

When soil water content changes, $${S}_{\text{MBC}}$$ needs to be estimated as follows: [Image Omitted. See PDF]

If the microbes at the wet microsites are in a potentially active state, the potentially active microbial biomass per unit volume of bulk soil decreases by maintenance respiration and biomass death and changes by MBC transformation between the dry and wet zones due to variations in soil water content: [Image Omitted. See PDF]where the parameter $$b$$ = 0.01, means that both the potentially active and dormant microbial maintenance respiration rates are two orders of magnitude lower than that of the active microbes.

The dormant MBC pool per unit volume of bulk soil decreases by maintenance respiration and changes by MBC transitions between the dry and wet zones due to variations in soil water content: [Image Omitted. See PDF]where $${R}_{\text{Dm}}$$ is the dormant microbial maintenance respiration rate at the dry microsites (g C m⁻³ s⁻¹). $${R}_{\text{Dm}}$$ is estimated as follows: [Image Omitted. See PDF]

The microbial heterotrophic respiration rate, $${R}_{h}$$ (g C m⁻³ s⁻¹), consists of the maintenance respiration of microbes in wet and dry zones, the respiration necessary to support EE production and growth respiration of the active microbes in the wet zone: [Image Omitted. See PDF]where $${R}_{g}$$ (g C m⁻³ s⁻¹) is the active microbial growth respiration rate at the wet microsites: [Image Omitted. See PDF]

ENZ Pool

The ENZ concentration per unit volume of soil, $${C}_{\text{ENZ}}$$ (g C m⁻³), comprises the bulk wet and dry ENZ concentrations: [Image Omitted. See PDF]

EE are produced by active microbes and are directly proportional to the DOC uptake rate (Schimel & Weintraub, 2003). The wet ENZ pool per unit volume of soil varies with enzyme production, enzyme turnover, and ENZ transitions between the dry and wet zones due to variations in soil water content: [Image Omitted. See PDF]where $${S}_{\text{ENZ}}$$ needs to be estimated as follows when the soil water content changes: [Image Omitted. See PDF]

The dry ENZ pool per unit volume of soil varies with enzyme turnover and transitions between wet and dry ENZs due to variations in soil water content: [Image Omitted. See PDF]

Noah-MP

Noah-MP is an augmented version of the Noah LSM with Multi-Physics (MP) options to facilitate testing competing hypotheses and climate predictions with processes-based ensembles (Niu et al., 2011). Noah-MP describes SOC decomposition using the first-order decay kinetics in a bulk soil layer (see Appendix A). In this study, Noah-MP operates with the dynamic vegetation option. To more accurately simulate the root autotrophic respiration and root carbon inputs to the SOC pool through exudates and dead roots at each soil layer, we (a) modified the dynamic vegetation model with layered roots in accordance with the soil layer thicknesses, (b) revised the evenly distributed root biomass profile of the original Noah-MP according to the observed global vertical distribution of roots for savanna (Jobbágy & Jackson, 2000), and (c) added the representation of root exudate rate as a constant proportion of root growth rate in the vegetation biomass balance, based on measurements of nearly up to 40% of photosynthetically fixed carbon being transferred to the rhizosphere through root exudates (Lynch & Whipps, 1990).

Incorporation of the Multi-Layer MESDM Into Noah-MP

The revised Noah-MP calculates soil temperature, volumetric water content, plant litter input rate and root exudation rate as well as the root autotrophic respiration rate in each soil layer. The plant litter input rate is determined by the turnover and death rates of the plant components. The root exudation rate is dependent on the photosynthetic rate and root biomass of the soil layer. The aboveground plant litter input is added into the SOC and DOC pools in the surface soil layer. The root litter and root exudation at each soil layer in the rhizosphere are added into the SOC and DOC pools in the corresponding soil layer.

The vertical layering of MESDM is consistent with that of the soil water and heat transfer model in Noah-MP. The multi-layer MESDM model defines different soil organic carbon pools and heterotrophic respiration rate at each soil layer. The gas transport model (see Appendix B) represents the O₂ and CO₂ gas concentrations through diffusion and advection in the vertical directions. We coupled the multi-layer MESDM with the O₂ and CO₂ gas transport model and further incorporated them into the revised Noah-MP. Thus, MESDM can simulate the various carbon pool sizes and heterotrophic respiration rate at each soil layer with the inputs of soil temperature and volumetric water content, plant litters input rate and root exudation rate modeled by the revised Noah-MP and soil O₂ concentration computed by the O₂ transport model. Accounting for the consumption of soil O₂ by microbial respiration, the O₂ transport model simulates the soil O₂ concentration profile controlled by soil temperature and water content (using constant atmospheric O₂ concentration). The CO₂ transport model simulates the soil CO₂ concentration profile and efflux at the surface accounting for CO₂ inputs from microbial heterotrophic and root autotrophic respirations and the effects of soil temperature and water content at each soil layer. Hereafter, Noah-MP coupled with the multi-layer MESDM is referred to as “new Noah-MP.”

Field Data and Model Experimental Setup Site and Data Description

The Santa Rita mesquite savanna site (31.8214°N and 110.8661°W; elevation 1,116 m) is a semiarid grassland that has been encroached by the native tree, velvet mesquite (Prosopis velutina), over the last century. It is located within the 215-km² Santa Rita Experimental Range (SRER; Elevations 884–1,585 m), 45 km south of Tucson, AZ, USA (Scott et al., 2009). The mean annual precipitation (1937–2007) is 377 mm, of which about 50% of the rainfall occurs from July to September and is associated with the North American monsoon (Scott et al., 2009). Within the footprint of an eddy covariance tower, the mesquite cover is approximately 35%; the total canopy cover of perennial C4 grasses, forbs and subshrubs is approximately 22%; and the remaining surface cover was bare soil. The yearly green-up of the plants associated with the monsoon typically begins around early July and involves large increases in the canopy cover of C4 warm-season grasses and summer annual grasses with comparatively smaller increases in the tree overstory. These perennial grasses grow most vigorously in July and August after the monsoon rains commence. Their roots are most dense in the upper 15 cm of the soil, but some roots extend deeper more than 60 cm (McClaran, 2003; Scott et al., 2009). The soils at the site are derived from Holocene alluvium from the erosion of igneous rocks. They are coarse to fine, deep, and well-drained with poor structure. At this site, in the Comoro series (coarse loamy, mixed thermic family of typic Torrifluvents; Tiedemann & Klemmedson, 1986), the soil is a loamy sand with sand and clay fractions of about 75% and 10%, respectively, on average in soil profile (while with sand of 84% and clay of 6% in the upper 10 cm). It has a total organic carbon fraction of less than 0.6%, with pH of 6, and a bulk density of 1.5 g cm⁻³ in the upper 10 cm under grass (Farella et al., 2020; McClaran et al., 2008; Wheeler et al., 2007).

The eddy covariance tower at this site provides a long-term data set of water, carbon, and energy fluxes and micrometeorology measurements at 30-min interval since 2004, and meanwhile, soil temperatures and volumetric water contents were observed at 5-, 10-, 20-, 30-, 50-, 70-, 100-, and 130-cm depths in an open area (data available at Ameriflux.lbl.gov, site name: US-SRM). The details of the instrumentation and data processing are fully described by Scott et al. (2009). The measured meteorological data include air temperature, wind speed, air humidity, pressure, incoming and outgoing longwave and shortwave radiation, and precipitation. The measured NEE (μmol m⁻² s⁻¹) is the difference between gross ecosystem production and ecosystem respiration (Reco).

At this site, Barron-Gafford et al. (2011) measured the volumetric CO₂ concentrations at depths of 2 and 10 cm of three microhabitats under mesquite, grass, and intercanopy space every 30 min through compact probes (GM222, Vaisala, Helsinki, Finland) throughout 2007. They calculated CO₂ efflux using the gradient of CO₂ concentrations measured at two depths, 2 and 10 cm, through Fick's first law of diffusion (Baldocchi et al., 2006). The derived soil CO₂ efflux values were then validated against measurements through chamber methods at least once every 2 weeks in the three microhabitats (Barron-Gafford et al., 2011).

Model Experimental Setup

We conduct model experiments for the case of an open area covered by the warm-season grasses. The new Noah-MP and the original one with the first-order-decay model are driven by the observed atmospheric forcing data for the entire year of 2007 to test against the measurements at the microhabitat under C4 grass at the Santa Rita site.

The soil column in Noah-MP is divided into 16 soil layers to a depth of 2 m to facilitate comparison with the measurements at various depths. A higher resolution is set up at the upper soil layers, with a topsoil layer thickness of 0.02 m and progressively a coarser resolution for deeper soil layers. The observation of the perennial warm-season grass roots in the SRER was used to initiate root biomass distributions (McClaran, 2003). The root exudate rate of warm-season grasses in the SRER was prescribed to be approximately 25% of the root growth rate (Lynch & Whipps, 1990). The fraction of litter from grasses allocated to SOC is about 0.9 with the remaining fraction being allocated to DOC (Campbell et al., 2016).

The soil water content and temperature at the 16 depths in the 2-m-deep soil column of the model are initialized by interpolating/extrapolating the measured values at eight depths. As a first-guess, the initial CO₂ and O₂ concentrations in the topsoil layer are set up as those of the surface atmosphere, and the O₂ concentration in the bottom soil layer is zero. Then, the initial CO₂ and O₂ concentrations at other depths are obtained by linearly interpolation and extrapolation using measured CO₂ concentration at the depths of 2 and 10 cm as well as the first-guessed values. We then spin up (iterate) the new Noah-MP driven by the one full-year atmospheric forcing data until the modeled profiles of O₂ and CO₂ concentrations, temperature, and soil moisture reach an equilibrium state to obtain more reasonable initial profiles.

The total organic C profile is initialized with the measured profile in the top 43.2 cm soil layer under the C4 grasses in SRER (McClaran et al., 2008; Wheeler et al., 2007) and the estimated organic C content of desert for the deeper soil (Jobbágy & Jackson, 2000). The initial total organic C is then allocated into SOC, DOC, and MBC in each soil layer according to the measured MBC and DOC concentrations at similar semiarid grassland sites (Parker & Schimel, 2011; Xiang et al., 2008), especially the Chihuahua Desert site experiencing the North American monsoon with both latitude (29.23°N) and mean annual precipitation (342 mm) being very close to the Santa Rita site (Van Gestel et al., 2016). The total ENZ concentration is set up to be about 4 g C m⁻³ according to the range (2.13–6.9 g C m⁻³) from a model study (Huang et al., 2018). Then these carbon pools are partitioned into sub-pools according to the relative water saturation through the spin-up run of the new Noah-MP. Finally, the equilibrium state of the sub-pool sizes are used as the initial values for subsequent model simulations. We initialize the fast and slow soil carbon pools in the first-order-decay model using the same initial total organic C concentration used in MESDM.

The parameters optimized for MESDM and their ranges from references are shown in Table 2. Some of the parameters from Allison et al. (2010) are prescribed for MESDM. We calibrate the model manually by tuning several parameters to obtain the highest Nash-Sutcliffe model efficiency (ME; an ME of 1 indicates a perfect simulation, an ME of zero means that the model is capable of representing the observed temporal mean, and a negative value indicates a poor simulation; Nash & Sutcliffe, 1970).

Table 2 Optimized Model Parameters With Prior Values and Ranges

Parameter	Unit	Value	Range	References
$${E}_{a}$$	J mol−1	4.7 × 104	4.7 × 104	Allison et al. (2010)
$${E}_{a_up}$$	J mol−1	4.7 × 104	4.7 × 104	Allison et al. (2010)
$${K}_{m0}$$	g C m−3	5 × 105	5 × 105	Allison et al. (2010)
$${K}_{\text{m0}\_\text{upDOC}}$$	g C m−3	102	102	Allison et al. (2010)
$${m}_{{K}_{m}}$$	g C m−3 °C−1	5 × 103	5 × 103	Allison et al. (2010)
$${m}_{{K}_{\text{m}\_\text{upDOC}}}$$	g C m−3 °C−1	10	10	Allison et al. (2010)
$$\sigma $$		0.5	0.5	Allison et al. (2010)
$${\tau }_{m}$$	s−1	5.56 × 10−8	5.56 × 10−8	Allison et al. (2010)
$$b$$		0.01		Blagodatskaya and Kuzyakov (2013)
$${E}_{\text{a}\_\text{mr}}$$	J mol−1	2.0 × 104	2.0 × 104	Van Iersel and Seymour (2002)
$${K}_{{\text{m}\_\text{upO}}_{2}}$$	m3 O2 m−3 air	0.121	0.121	Davidson et al. (2012)
$${k}_{e}$$		0.5%	1–5%	Burns et al. (2013) and Schimel and Weintraub (2003)
$${m}_{\varepsilon }$$	°C−1	−0.011		This study
$${T}_{\text{ref}}$$	K	283.15		Huang et al. (2018)
$${V}_{\mathrm{max}0}$$	g C m−3 (g C m−3)−1 s−1	4.0 × 10−4	2.8 × 10−5–5.6 × 10−3	Wang et al. (2019)
$${V}_{\text{max0}\_\text{up}}$$	g C m−3 (g C m−3)−1 s−1	5.0 × 10−5	2.78 × 10−6–5.5 × 10−4	Huang et al. (2018) and Moyano et al. (2018)
$${V}_{\text{0}\_\text{mr}}$$	g C m−3 (g C m−3)−1 s−1	2.0 × 10−6	2.78 × 10−7–2.24 × 10−5	He et al. (2015) and Kaiser et al. (2014)
$$\alpha $$		0.9	0.9	Campbell et al. (2016)
$${\varepsilon }_{e}$$		0.4		Alster et al. (2013)
$${\varepsilon }_{0}$$		0.5	0.5	Allison and Goulden (2017) and Schimel and Weintraub (2003)
$$\eta $$		0.6		This study
$$\lambda $$		0.1		Blagodatskaya and Kuzyakov (2013)
$${\tau }_{e}$$	s−1	6.5 × 10−8	2.31 × 10−8–1.16 × 10−6	Schimel et al. (2017), Tang and Riley (2015), and Wang et al. (2019)

Results

We use the ME, root mean square error (RMSE), and correlation coefficient (R) to measure the model's skill at capturing the observed variability throughout the paper.

Soil Temperature and Moisture

The observed air temperature at 2.5 m increased and reached its peak values at midday hours prior to the onset of the monsoon (day 181), and more than 70% of the annual precipitation in 2007 was attributed to the rain pulses during the summer monsoon (Figure 2a). The modeled volumetric soil water contents at 5 and 10 cm match well the half-hourly observed values, except for some overestimated peaks in response to the monsoon rainstorms, with the ME values over 0.85 and the R values of 0.95 (Figures 2b and 2c). The simulated soil temperatures at 5 and 10-cm depths are in good agreement with the half-hourly observed values, especially during the monsoon season with high transpiration and sheltering by the growing plants, resulting in a good model performance with the ME values above 0.93 and the R values of 0.98, even though it underestimated the nighttime lowest values during the long drought period before the monsoon (Figures 2d and 2e). In addition, according to the statistical values, the model perform better in simulating the soil water content and temperature in deeper soil layers than in shallow soil layers. Overall, the statistics reflect that both the modeled soil moisture and temperature are satisfying to drive the microbial respiration simulations (Figures 2b–2d).

Figure 2. Observed half-hourly air temperature and precipitation (a), observed (obs; blue dotted line) and simulated (sim; red solid line) half-hourly volumetric soil moisture at 5 cm (b) and 10 cm (c), and observed (blue dotted line) and simulated (red solid line) half-hourly soil temperature at 5 cm (d) and 10 cm (e) at the Santa Rita site in 2007. ME = model efficiency; RMSE = root mean square error; and R = correlation coefficient.

CO₂ Concentration and Efflux

The original Noah-MP equipped with the bulk-layer, first-order decay model does not have a capability of modeling the CO₂ concentration at each soil layers. The modeled CO₂ effluxes are underestimated in winter when the soil temperature was relatively lower (e.g., Day 1–60 and Day 330–365; Figure 3a), whereas they are overestimated prior to the monsoon onset (e.g., Day 120–180) when the daily maximums of soil temperature at 5-cm depth exceeded 40°C (Figures 2d and 3a). This indicates that the base rate of the first-order decay model may be too low or that the model does not sufficiently represent the soil moisture constraint on the temperature sensitivity of soil respiration during the drought period. For the same reason, the original model always underestimates nighttime effluxes during the monsoon season (Day 181–270). Although the modeled effluxes shows some weak responses to the soil moisture pulses during the middle and late monsoon seasons, the original Noah-MP generally fails to reproduce the observed pulse responses of soil respiration to the soil moisture pulses during the early monsoon season and in winter.

Figure 3. Simulated (sim; red solid line) half-hourly soil CO2 efflux by Noah-MP with the original first-order decay model (a), and simulated half-hourly soil CO2 efflux (b) and soil CO2 concentrations at depth of 2 cm (c) and 10 cm (d) by Noah-MP with microbial-explicit soil organic carbon decomposition model at the Santa Rita site in 2007 compared with observations (obs; blue dotted line).

The modeled CO₂ effluxes and concentrations at 2 and 10-cm depths by the new Noah-MP model with MESDM agree well with the observed values throughout the year. In response to each precipitation event of different sizes, especially during the monsoon season, the new model reproduces the observed Birch effect in terms of timing and magnitude except some overestimated peaks of the respiration pulses corresponding to the larger-than-observed peaks of the modeled soil moisture in the top 5-cm soil layer when precipitation occurs (Figure 2a). However, because most of the overestimated peaks occur in one 30-min time step, the resulting errors are negligible. Moreover, during the long pre-monsoon drought with extremely high temperatures and volumetric water contents less than 0.03 m³ m⁻³, the simulated CO₂ effluxes are much closer to the observed values than the simulated values by the old model. Hence, the new Noah-MP model has high MEs above 0.72 and Rs above 0.86 (Figures 3b–3d).

The cumulative CO₂ efflux at the soil surface measured under the C4 grass at this site over 2007 is ∼302 g C m⁻² (excluding the missing data). Corresponding to the observed data, the original model underestimates the cumulative CO₂ efflux by 55%, whereas the new model significantly reduces this bias (only −3.7% lower; Figure 4). The original model starts to underestimate the efflux from the very beginning, and the underestimation becomes dramatically large during the monsoon for not well reproducing the observed pulse response to the monsoon rainfall pulses (Figure 4). However, the cumulative efflux simulated by the new model is much more consistent with the observed during the monsoon season, and then the underestimation of about 11.24 g C m⁻² occurs mostly during the hot and dry post-monsoon period (after Day 270).

Figure 4. Observed (black solid line) and simulated cumulative half-hourly C effluxes at soil surface by Noah-MP with the original soil carbon model (blue dish-dotted line) and microbial-explicit soil organic carbon decomposition model (red dashed line) at the Santa Rita site in 2007 (the modeled values corresponding missing observed data are excluded to calculate the cumulative efflux).

Soil Microbial and Root Respirations

Soil CO₂ production is composed of soil microbial heterotrophic and root autotrophic respirations. The simulated cumulative soil CO₂ production is roughly equal the simulated cumulative surface CO₂ efflux, which is caused by the fairly fast transport processes and the negligible role of soil CO₂ storage capacity (see Figure S1 in Supporting Information S1). The simulated microbial heterotrophic respiration rate more apparently follows the variations in soil moisture, while the simulated root autotrophic respiration (including maintenance and growth respiration) shows a more apparent diurnal variation, which is dominated by the diurnal variations in temperature and solar radiation during the growing season (Figures 5a and 5b). Because the root respiration substantially contributes to the diurnal variation in the soil surface CO₂ efflux, the model errors in the simulated CO₂ efflux, caused by a diurnal range larger than the measurements from day 210–240 (Figure 3b), are mainly attributed to the simulated root respiration (Figure 5b). In contrast to the relatively weak pulsed responses of the daytime root respiration peak, the MESDM-simulated microbial respiration dominates the contribution to the simulated soil efflux pulses in response to rainfall pulses (Figure 5a). During the dry season prior to the onset of the monsoon, the modeled daily mean microbial respiration rates accounts for over 95% of soil surface CO₂ effluxes, and during the growing season this ratio varies in a range of 80%–40%, indicating a substantial contribution of the microbial respiration to soil CO₂ efflux (Figure 5c).

Figure 5. Microbial-explicit soil organic carbon decomposition model (MESDM)-simulated half-hourly microbial heterotrophic respiration rate in the entire soil profile (RH) (a), root autotrophic respiration rate in the root zone (RA) (b) and ratio of daily mean RH to the total soil respiration (RA+RH) (c) by Noah-MP with MESDM at the Santa Rita site in 2007.

NEE

We use the half-hourly NEE data measured with the eddy covariance method to confirm the improved performance of MESDM. Figure 6 shows the NEE simulations for Days 180–300, including the growing season of C4 grasses, in response to the summer monsoon (Scott et al., 2009). Positive upward NEEs comprise microbial heterotrophic and vegetation autotrophic respiration at night. The original Noah-MP significantly underestimates most of the positive NEEs due to its underestimation of soil CO₂ efflux (Figure 6a). As a result, the underestimation of soil CO₂ efflux results in overestimated downward NEEs in the daytime. But, the new Noah-MP better captures the nighttime positive NEEs during the growing season due to the new model's capability of reproducing soil CO₂ efflux pulses in response to precipitation pulses (Figure 6b). Hence, the simulated negative NEEs are much closer to the measured values than those simulated by the original model. The new Noah-MP model shows a better capability of simulating NEE as a result of the better performance of MESDM with higher ME (0.62) and R (0.84).

Figure 6. Observed (obs; blue dotted line) and simulated (sim; red solid line) half-hourly net ecosystem exchanges during the monsoon season by Noah-MP with the original Noah-MP soil carbon model (a) and microbial-explicit soil organic carbon decomposition model (b) at the Santa Rita site in 2007.

Evolution of Modeled DOC, MBC, ENZ, and SOC Pools

Evolutions of the modeled wet and dry carbon pools per unit volume of bulk soil in the top 13-cm soil layer (the top 4 soil layers) show very different patterns in the wet and dry seasons (shown in Figure 7). The modeled wet carbon pools of DOC, ENZ, and MBC are much smaller than their corresponding dry carbon pools. In response to soil moisture pulses, the wet and dry carbon pools show opposite pulses due to the transitions between the wet and dry carbon pools. The variations in the wet pools exhibited similar patterns to that of the 5 and 10-cm volumetric water contents.

Figure 7. The evolutions of the microbial-explicit soil organic carbon decomposition model-simulated bulk concentrations of the wet (blue line), dry (red line), and total (black line) carbon pools of dissolved organic carbon (a), microbial biomass carbon (b), ENZ (c), and soil organic carbon (d) in the top 13-cm soil layer at the Santa Rita site in 2007.

The dry ENZ concentration exhibit a slow decline during the pre-monsoon dry seasons (Figure 7c). This helps continuously produce dry DOC at relatively steady depolymerization rates so that the bulk dry DOC progressively increases to its peak values of 315.04 g C m⁻³ by the end of the longest droughts of about 84 days before the monsoon (Figure 7a). Similarly, DOC accumulates to 256.19 g C m⁻³ over the 53-day drought after monsoon season. A longer drought period before a precipitation event results in a greater accumulation of dry DOC. After the onset of the monsoon, the dry DOC quickly declines to 98.69 g C m⁻³ (Figure 7a). The total MBC declines by over 40% during the pre-monsoon dry season relative to its initial value. Over monsoon season, the dormant MBC obviously shows a net increase resulting from a net transition from wet to dry MBCs (Figure 7b), because the active MBC experiencing fast growth following wet DOC pulses has larger concentration at the reaction microsite than the dormant MBC for most of the time (see Figure S3 in Supporting Information S1). Moreover, in the early cold winter, the active MBC rapidly increases due to high CUE at lower temperatures when rainfalls bring about pulses of the wet DOC. Similarly to the dormant MBC, the net transition from wet to dry ENZs promotes an increase in the dry ENZ (Figure 7c), while the wet ENZ is greater than the dry at the reaction microsite due to EE production (Figure S3 in Supporting Information S1). During the wet season, variations in wet MBC/ENZ are generated from both the transitions between the dry and wet MBCs/ENZs as well as growth/EE production. Taken together, in the whole year, the modeled MBC and ENZ have the similar evolving patterns that are completely different from that of the modeled DOC.

The modeled SOC pool in top 13-cm soil layer gradually decreases by 325 g C m⁻³ until the beginning of the growing season due to depolymerization losses from enzymatic catalysis and then increases with a SOC input rate mostly from grass litter that is greater than the decomposition rate (Figure 7d). By the end of the year, the total MBC and ENZ approach to their corresponding initial values, and the total DOC concentration is approximately 55.48 g C m⁻³ larger than its initial value, while the SOC concentration increases by 331.36 g C m⁻³ relative to its initial value. In brief, modeled DOC, MBC, ENZ, and SOC pools exhibit obvious seasonal variations.

Discussion Model Parameters

In this study, most model parameters involved in the depolymerization and uptake rates are consistent with those used in previous studies (Allison, 2014; Allison et al., 2010; Davidson et al., 2012). Some parameters that are calibrated in our simulation are within the ranges found in literatures (Table. 2). The enzyme turnover rate constant of MESDM (6.5 × 10⁻⁸ s⁻¹) is in the observed range from 2.31 × 10⁻⁸ to 1.16 × 10⁻⁶ s⁻¹ (Schimel et al., 2017) and at a same magnitude with those used in Tang and Riley (2015) and Wang et al. (2019). However, an order of 10⁻⁷ for the enzyme turnover rate constant, which is a highly sensitive parameter, would lead to a rapid decline in the dry and wet ENZs down to zero before the monsoon, because the enzyme production rate is much less than the turnover rate due to an average of 97% of microbes being in dormancy during the pre-monsoon hot drought (Figure S2 in Supporting Information S1). However, stable and enhanced enzyme pools during droughts observed by Steinweg et al. (2013) and Alster et al. (2013) support a much lower enzyme turnover in dry soils (Blankinship et al., 2014). The value of the dry-zone enzyme turnover rate in MESDM is assumed to be 2/3 of the value in the wet zone. A proportion of 0.5% of the DOC taken up by active microbes is used for EE production in this study; this value results in realistic simulations, even though it is less than the estimated value (1%–5%) from relevant literatures (Burns et al., 2013; Schimel & Weintraub, 2003). The value of enzymatic catalysis efficiency at the dry microsites is estimated to be 40% of that at the wet microsites according to Alster et al. (2013). The intercept of CUE as a linear function of temperature in our study is referred to the value in DEMENT that had been used to study the drought tolerance of microbial decomposition (Allison & Goulden, 2017), and the value of the slope is chosen to be approximately 0.011°C⁻¹ because larger values indicate negative CUE with high temperatures (>45°C).

Responses of Total MBC, DOC, and ENZ to Drought and Rewetting

At present, the MBC and DOC concentrations and potential EE activities in the bulk soil are measurable, but there are no available data at the Santa Rita site. Thus, as an indirect evaluation of model performance, we discuss the seasonal evolving patterns of the simulated total MBC, DOC, and ENZ in the top 13-cm soil layer at Santa Rita site with the observations at other sites with similar semiarid grassland soils.

Response to Droughts

The MESDM-simulated total DOC accumulation is mostly contributed by the bulk dry DOC accumulation as a result of sustained dry EE activity during drought periods (Figure 7a). Moreover, the simulated total DOC accumulation increases with the length of the drought. This is consistent with observations during summer dry seasons in both laboratory and other field experiments (Homyak et al., 2018; Schaeffer et al., 2017; Xiang et al., 2008). Additionally, our simulated maximum value of total DOC concentration, ∼315 g C m⁻³, in the top 13-cm soil layer prior to the onset of the monsoon (Figure 7a) is very close to the observed maximum values of water-extractable organic carbon (WEOC) ranging from ∼240 to 300 g C m⁻³ in the upper 10-cm soil during the 2004 dry season at the California grassland plots (Homyak et al., 2018).

As expected, MESDM simulates declines in the total MBC and ENZ in the top 13-cm soil layer during the drought period due to the moisture stress on microbial survival (Schimel, 2018; Figures 7b and 7c). At the Santa Rita site, during the pre-monsoon hot drought period of over 75 days when the observed midday ground surface temperatures mostly exceeded 50°C and the 0 to 10-cm volumetric soil water content was less than 0.03 m³ m⁻³ (Barron-Gafford et al., 2011), nearly 97% of the simulated total MBCs are in dormancy (Figure S2 in Supporting Information S1). The sum of the dormant microbial maintenance respiration and the active microbial mortality surpasses the negligible growth of the active microbes, resulting in the modeled decline in total MBC. The marginal active microbes assimilate wet DOC at a much lower rate and produce EE less than its turnover, so that total ENZ reduces gradually during the drought periods. This is in agreement with the observed decrease in soil potential enzyme activity with drought in field experiments (Steinweg et al., 2012).

However, in the California grassland, both the observed MBC and potential enzyme activities showed increases in the middle-late dry season (Alster et al., 2013; Homyak et al., 2018; Parker & Schimel, 2011; Schaeffer et al., 2017). In California grassland soils of Sedgwick Reserve, average 0–10 cm soil moisture almost linearly decreased about from 0.12 to 0.07 m³ m⁻³ during a 5-month dry season of 2014 (Homyak et al., 2018). At this Reserve, both the observed MBC (about 300 g C m⁻³) and total organic carbon concentrations (2.4 × 10⁴ g C m⁻³) were about three times the MESDM-simulated MBC (90 g C m⁻³) and total organic carbon (7.6 × 10³ g C m⁻³) in the top soil layer at the Santa Rita site, respectively, at the beginning of the dry season (the measured values of total organic carbon at SRER are from 7.1 × 10³ to 8.5 × 10³ g C m⁻³ in Wheeler et al. (2007) and McClaran et al. (2008)). It is most likely because of the higher water content, more active MBC during the dry season are able to assimilate more DOC for producing more EE and sustaining a high microbial growth rate that outweigh the sum of active microbial mortality and dormant microbial maintenance respiration. These may explain the observed increase in MBC in the California grassland soils (Homyak et al., 2018; Schaeffer et al., 2017). Furthermore, when the EE production rate equals or surpasses the total ENZ turnover rate, the total ENZ controlling the potential enzyme activity becomes stable or increases, which has been observed in enzyme assays in response to droughts in other field experiments (Steinweg et al., 2013) and at other California grassland site (Alster et al., 2013). To mimic the increases in MBC and ENZ during drought periods, we conduct a model experiment that is same as the one of running new Noah-MP at the Santa Rita site, but with manually maintaining average 0–13 cm volumetric soil moisture content about 0.09 m³ m⁻³ (average volumetric water content in the California grassland soils during the 5-month dry season) during a 3-month drought (Figure S4 in Supporting Information S1). The modeling results show slight increase in both total MBC and ENZ during the middle-late drought. But relative to the original model experiment, lower DOC accumulates prior to the monsoon (Figure S5 in Supporting Information S1). These confirm the above explanations for the California grassland. In short, soil moisture controls the evolution of total MBC and ENZ and accumulation of DOC during dry seasons through the effects of soil moisture on the fractions of active MBC and dry ENZ.

Response to Rewetting

After the onset of the pulsed monsoon precipitation at the Santa Rita site, the simulated total DOC in the top 13-cm soil layer declines quickly, approaching its initial value at dry season, as a result of the net transition from the dry to wet DOC pools in response to rainfall events (Figure 7a). This decline in total DOC upon wetting agrees with the observed decrease in WEOC with the start of winter rainy seasons in the California grassland soil (Homyak et al., 2018; Schaeffer et al., 2017). During the monsoon season, when more active MBC and higher DOC at the wet microsites upon rewetting brings about higher DOC uptake rate, microbial assimilation meets the requirements of not only EE production and maintenance respiration but also growth of active microbes. Thus, the simulated total MBC shows an obvious increase after wetting at the Santa Rita site (Figure 7b). This increase in MBC in the top soil layer has also been observed with the start of winter rainy seasons in the California grassland soils (Homyak et al., 2018) and in the laboratory dry-wet cycle experiments (Xiang et al., 2008). However, when the accumulated DOC prior to the wet season were not high enough or the available DOC were quickly consumed to a low value, the microbial assimilation would maintain a low active microbial growth rate that may be less than the sum of the active microbial mortality and the dormant microbial maintenance respiration. In particular, in the case of soil experiencing large water content variations upon rewetting with high MBC, more dormant MBC is activated into an active state, leading to a higher rate of active microbial mortality. These mechanisms may be the causes of the observed decreases in MBC in the California grassland soils in early (Parker & Schimel, 2011; Schaeffer et al., 2017) and late winter rainy seasons when the average volumetric soil water content was above 0.3 m³ m⁻³ (Homyak et al., 2018).

With increasing microbial assimilation rate of available DOC after rewetting at the Santa Rita site, the active microbes produce more EE than they do during the antecedent drought. When EE production rate is larger/lower than turnover rate, the simulated total ENZ increases/reduces during the early/late monsoon (Figure 7c), consistent with the observed potential enzyme activities following the early/late monsoon rain in the Chihuahuan Desert soils (Ladwig et al., 2015). Taken together, both the amount of DOC accumulation during the dry season and rewetting intensity regulate the evolution of total MBC and ENZ during the wet season, by activating the dormant microbes and increasing the DOC uptake rate that determines microbial growth and EE production rates.

Microbial Heterotrophic Respiration Response to Hot Drought and Rewetting Response to Hot Drought

During the 2-month drought periods prior to the onset of monsoon, the simulated microbial heterotrophic rate is very low at the Santa Rita site, because on average over 97% of the microbes are in dormancy at a low maintenance respiration rate (Figure 5a and Figure S2 in Supporting Information S1). Moreover, the temperature response of much low dormant microbial maintenance respiration rate is imperceptible. In addition, our model accounts for microbial transitions from active into the potentially active states in the wet zone in response to extremely high temperature. Thus, the simulated microbial respiration rate does not increase with the high temperatures during the hot droughts before the monsoon as does the original first-order decay model. This suggests that MESDM has a good capability of representing the soil moisture constraint on the temperature sensitivity of soil microbial respiration, which is not well represented in current ESMs (e.g., Arora et al., 2020).

Response to Rewetting—The Birch Effect

The mechanisms underlying the Birch effect have been explored through laboratory and field experiments as well as model studies but are still unclear (Schimel, 2018). One of the important mechanisms is that the accumulated DOC in dry soil may fuel the respiration pulses upon wetting (Blankinship et al., 2014; Manzoni et al., 2014; Parker & Schimel, 2011; Stursova & Sinsabaugh, 2008). Another mechanism is that dormant microbes in dry soils are metabolically reactivated within minutes or hours in response to rewetting (Evans et al., 2016; Liu et al., 2019; Manzoni et al., 2014; Placella et al., 2012; Salazar et al., 2018; Salazar-Villegas et al., 2016). Based on observational and modeling studies, it is most likely that these two mechanisms are at play in the Birch effect (Schimel, 2018). Here, we implement these two mechanisms into MESDM by assuming that enzymes remain active at the dry microsites with reduced enzymatic catalysis efficiency and that the dormant microbes at the dry microsites are transitioned into a metabolically active state upon rewetting.

In our simulation results, the continuing EE activities at the dry microsites produce dry DOC that is inaccessible to active microbes at the wet microsites, which results in the accumulation of dry DOC during long- or short-term droughts. Upon rewetting, the transition from dry to wet DOCs and reactivation of a portion of dormant microbes occur, providing more DOC for more active MBC to mineralize into CO₂ (Figures 5a and 7). When the soil is drying, the wet DOC rapidly decreases caused by both the transition from wet to dry DOCs and consumption from DOC uptake, while the active MBC gradually decreases due to the transition to microbial dormancy state despite simultaneous microbial growth, which results in the decrease in microbial respiration rate (Figures 5a and 7). As a consequence, throughout the whole year, both simulated wet DOC and active MBC pulses correspond to the simulated microbial respiratory pulses of varying sizes under soil wetting-drying cycles at site (Figure 5a). Especially, during the middle monsoon, when the soils at 5 and 10 cm depths are almost the wettest of the whole year and the simulated active MBC prior to the rainfalls is the largest of the summer, the simulated wet DOC and active MBC pulses of smaller sizes still bring about the relative large microbial respiratory pulses with high baseline respiration rate (Figure 5a). Obviously, our simulation results suggest that these two mechanisms jointly contribute to the Birch effect.

DOC accumulation in dry soils becoming bio-available upon rewetting as a mechanism for the Birch effect has been supported by both experimental observations and models (Evans et al., 2016; Lawrence et al., 2009; Liu et al., 2019; Manzoni et al., 2014, 2016; Zhang et al., 2014). A number of studies have observed DOC accumulation during dry seasons and declines in DOC during wet seasons and suggested that the accumulated DOC becomes available for microbes upon rewetting, resulting in the immediate respiration pulses (Homyak et al., 2018; Schaeffer et al., 2017; Steinweg et al., 2013; Xiang et al., 2008). Based on the hypothesis that the continuing EE activities in dry soils can produce DOC, a few microbial-explicit models have modeled DOC accumulation because of reduced microbial uptake (Lawrence et al., 2009), diffusion limitations (Evans et al., 2016; Manzoni et al., 2014), and/or inaccessibility by microbes (Zhang et al., 2014) and hence produced the Birch effect. Even considering DOC accumulation alone, microbial models have successfully simulated the Birch effect (Lawrence et al., 2009; Zhang et al., 2014). Thus, DOC accumulation has been regarded as the predominant control on the Birch effect (Manzoni et al., 2014). Model results from Evans et al. (2016) accounting for microbial dynamics suggested that DOC accumulation is important for the size of respiration pulses. MESDM is able to simulate the increase in DOC with dry season length, which is consistent with results from other model (Manzoni et al., 2014) and experiments (Homyak et al., 2018; Miller et al., 2005; Schaeffer et al., 2017; Steinweg et al., 2013; Xiang et al., 2008). Importantly, our model simulates the timing and size of microbial respiratory pulses in a good agreement with the observations at the Santa Rita site. Here, we emphasize that DOC accumulation in dry soils becoming bio-available upon rewetting is a major mechanism for the Birch effect at this site.

The mechanism of activation of dormant microbes upon rewetting has been recognized to be responsible for the Birch effect from experimental and model studies. Rewetting experiments have supported that the activation of dormant microbes contributes to the respiratory pulses (Placella et al., 2012; Salazar-Villegas et al., 2016). Microbial dormancy and reactivation have been incorporated into microbial-explicit models to improve the simulation of the Birch effect using empirical functions of soil moistures (Evans et al., 2016; Liu et al., 2019; Manzoni et al., 2014; Salazar et al., 2018). Our model represents the active and dormant microbes in a more explicit way according to whether they are at the wet or dry microsites of soil pores. The changes in the volumes of the wet and dry microsites determine the transition between active and dormant microbes, caused by the change in soil water saturation. Thus, not the microbial reaction rates at the microsites but the bulk reaction rates are dependent on soil moisture content. It is more physiologically explicit to represent how soil moisture exerts an influence on the changes of active and dormant MBC as well as microbial reaction rate. This explicit representation of soil moisture controls on microbial physiological state (Marschner & Kalbitz, 2003) is completely different from those in existing microbial dormancy model using empirical functions of soil moisture.

In our simulation results, active MBC pulses contribute to the microbial respiration pulses in response to the rainfalls at the site (Figure 7b). The active MBC fraction in top 13-cm soil layer drops to on average 2% during 2-month drought prior to monsoon, and the peak of active MBC fraction after rewetting ranges approximately from 16% to 42% during the monsoon period (Figure S2 in Supporting Information S1). In recent model studies, the peaks of active MBC fractions were reported to be less than 5% in Salazar et al. (2018) and more than 80% in both Liu et al. (2019) and Manzoni et al. (2014). Numerous studies show that the active fraction is very likely below 50% of live microbes under most natural soil conditions (Blagodatskaya & Kuzyakov, 2013; Wang et al., 2014). Hence, it is suggested that the variation of MESDM-simulated active MBC fraction is relatively reasonable under continuously drying-rewetting cycles during the monsoon period. Compared to Zhang et al. (2014) without including microbial dormancy, MESDM simulates realistically larger MBC throughout the whole year at the Santa Rita site. Salazar et al. (2018) have shown similar simulation results that no consideration of microbial dormancy and reactivation mechanisms brings about the more severe decline in MBC when undergoing four drying-wetting cycles. It can be explained that when soil is drying, MBC, if all remaining active, may decrease much more dramatically than if a portion remains active, due to larger active microbial mortality and maintenance consumption. Our simulation results demonstrate that, ignoring the dormancy in MESDM, the initial MBC rapidly declines to zero before the monsoon at the Santa Rita site (with the same model parameters and initial values, figures not shown). Taken together, the dormancy mechanism helps avoid the severe decline in MBC in dry seasons, supporting more active microbes to take up DOC at a higher rate that results in respiration pulses and more EE production upon rewetting. In turn, EE production after rewetting sustains ENZ supporting DOC accumulation in subsequent dry seasons. Apparently, these two mechanisms jointly contribute to the Birch effects under continuous drying-rewetting cycles at the Santa Rita site.

Model Limitations and Uniqueness Model Limitations

In MESDM, the bulk soil of each layer is divided into the dry and wet zones, and soil water only exists in the wet zone, where DOC in the soil solution is transferred to active microbial cells through diffusion processes. We assume that the substrate diffusion processes, which are regulated by both the solute density gradient and diffusivity coefficient of the solution in the wet zone, are quite faster than the slow processes of microbial uptake, so that the DOC concentration can rapidly reach an equilibrium state in the soil solution of the wet zone (Zhang et al., 2014). Thus, we neglect the limitation of DOC diffusion in the soil solution on the microbial uptake rate at the reaction microsites in MESDM. Here, MESDM does not account for soil organic carbon stabilization determined by adsorption to mineral surfaces and aggregate formation at the Santa Rita site with low clay content of less than 10%.

MESDM relies on accumulation of DOC during the dry period and reactivation of dormant microbes upon rewetting to reproduce the observed Birch effect. Implementing the hypothesis of continuing EE activities, into MESDM substantially produces the simulated dry-season DOC accumulation. However, this hypothetical mechanism is not well verified with experimental evidence, and thus MESDM may simulate well the Birch effect for wrong reasons. Homyak et al. (2018) tended to reject the hypothesis that the sustained exoenzyme-driven decomposition of plant litter produces WEOC accumulation as soils dry, through observations from field and laboratory experiments. Their field observations showed WEOC accumulation in plots without plants (plant removal) was significantly larger than that in plots with plants during the dry season in the California grassland. In their 4-week laboratory incubation, reducing sugars did not accumulate in dry senesced roots. Nevertheless, in their field plots without plants, there were still particulate organic carbon and mineral-associated organic carbon in the soils despite no plant litter inputs. In their laboratory incubations, the dry root segments (1-cm long) were significantly different in surface areas and chemistry from equivalent leaf litter or particulate organic carbon at 10²–10³ $${\mu}\mathrm{m}$$ scales in the soils (as presumably represented in models). In that way, actual enzyme activities may not be identical among the three kinds of organic carbon under dry conditions. Hence, their observations do not falsify the hypothesis that continuing EE activities degrade SOC and produce DOC accumulation in the soils during the dry period. We call for well-designed experiments to test this hypothesis in future studies considering the limitation of model application.

In addition, some studies pose a hypothesis of the aboveground litter photodegradation for DOC accumulation (Austin & Vivanco, 2006; Barnes et al., 2012). But, the effect of photodegradation is highly reduced through dust deposition on surface leaf litters at the Santa Rita site (Barnes et al., 2012). Furthermore, observed respiratory pulses at 2- and 10-cm depths suggest underground DOC accumulation. Therefore, photodegradation of the aboveground litter may be not a primary mechanism of DOC accumulation at this site. But, in MESDM, neglecting photodegradation may lead to an underestimation of the decomposition rate, because photodegradation may contribute to the aboveground litter decomposition despite reduced effects of dust deposition (Austin & Vivanco, 2006). This is most likely one of the reasons that the MESDM-simulated cumulative CO₂ flux was underestimated after the growing season, when the plant litter input rate was much larger than that during the growing season at the Santa Rita site.

Transport of DOC and ENZ solutes as well as microbial colloids through infiltration in soil pores is one of the major resources of SOC in deeper soils. When precipitation occurs, water may infiltrate through macro-pores (or macro-channels), which are formed by dead roots and/or aggregates during drying-wetting cycles, into deep soil layers at a much faster rate than the soil matrix flow alone (Beven & Germann, 2013). In this study, MESDM neglects solute and colloid transport processes with both macropore and matrix flows, causing errors in simulated DOC, ENZ, and MBC, which may be overestimated in the upper soil layers and underestimated in the deeper soil layers.

MESDM does not take into account complex plant litter decomposition processes (e.g., different activation energy required for depolymerization of the labile, cellulose and lignin contained in the litters) and simply incorporates litter into the soil layer by separating litter organic carbon into SOC and DOC pools. This simple treats may produce an overestimation of litter decomposition rate in this study.

Model errors due to uncertainties in the representations of the above complex processes involved in SOC decomposition may lead to confusion that make it difficult to identify which process the errors may come from, especially when observational data are not enough to test the representations of each process. Hence, we neglect some processes and focus on clarifying the main mechanisms underlying soil heterotrophic respiration pulses in response to drying-wetting cycles at the Santa Rita site in a semiarid grassland through the model experiments.

Model Uniqueness

Soil biology and biogeochemical characteristics has been considered spatially heterogeneous at the microsite scale (Wanzek et al., 2018). It has been recognized that differences in the carbon pool concentrations at the reaction microsites, which are regulated by redistribution of soil water in the soil pores, generate different reaction rates according to the Michaelis-Menten kinetics (Davidson et al., 2012; Moyano et al., 2018). To estimate the soil carbon decomposition rate at the soil bulk-scale, accounting for the differences at the reaction microsites in soil pores is critical for scaling up the pore-scale microbial model in LSM for use in ESMs. In MESDM, differentiation of wet and dry zones is a first attempt to describe the differences in concentrations of various carbon pools and reaction rates between the wet and dry microsites. Because the ratio of the modeled carbon pool concentration at the wet or dry microsites to the bulk concentration is proportional to the reciprocals of $$w$$ or $$(1-w)$$, respectively, the differences in the modeled carbon pool concentration between soil microsites and bulk soil vary with soil moisture by up to two orders of magnitude (Figure 7 and Figure S3 in Supporting Information S1). MESDM uses carbon pool concentrations at the reaction microsites to calculate the reaction rates in the wet and dry zones with the Michaelis-Menten kinetics. It is notable that the calculated bulk reaction rate using carbon pool concentrations at the reaction microsites (e.g., bulk DOC uptake rate: $$\frac{{C}_{\text{MBC}\_\text{WA}}\cdot {C}_{\text{DOC}\_\text{W}}}{{K}_{\text{m}\_\text{upDOC}}+{C}_{\text{DOC}\_\text{W}}}\cdot w$$) is larger than that using the bulk concentration $$(\frac{{C}_{\text{MBC}\_\text{WA}}\cdot w\cdot {C}_{\text{DOC}\_\text{W}}\cdot w}{{K}_{\text{m}\_\text{upDOC}}+{C}_{\text{DOC}\_\text{W}}\cdot w})$$ in the Michaelis-Menten equation. Additionally, because of the differentiation of wet and dry microsites, there is no need to consider moisture effects on the maximum uptake rate and the half-saturation when using Michaelis-Menten kinetics to estimate the DOC uptake rate using DOC and active MBC concentrations at the wet microsites, whereas the half-saturation is assumed to be not moisture-dependent in a few model (Davidson et al., 2012; Manzoni et al., 2016).

Conclusions

We developed a MESDM with a high vertical resolution and half-hourly time step. MESDM accounts for soil moisture controls on microbial and enzymatic processes, the transitions between the wet and dry DOCs/ENZs, and the transformation between active and dormant or potentially active microbes at soil wet and dry microsites of soil pores by dividing the soil volume into the wet and dry zones. MESDM, incorporated into Noah-MP LSM in place of the first-order decay model, can successfully reproduce the timing and size of soil respiratory pulses (Birch effect) in response to episodic rainfall pulses and significantly improve the simulations of NEE at the Santa Rita site in a semiarid grassland. The modeled DOC, MBC, and ENZ concentrations are reasonable when compared with observations at other field sites with similar soils and climates. MESDM improves the simulation of soil moisture sensitivity of SOC decomposition, which helps constrain its temperature sensitivity under a warming climate experiencing more frequent and intense droughts. In addition, differentiation of wet and dry microsites in the soil pore is a feasible approach to scaling up the pore-scale microbial processes in LSM.

We found that the accumulation of DOC during the dry period and the activation of dormant microbes upon rewetting are the dominant mechanisms responsible for the Birch effect at the semiarid grassland site. Implementing the hypothetical mechanism of continuing EE activities in drying soils into MEDSM can produce the modeled DOC accumulation and hence the modeled Birch effect at this semiarid grassland site with a relatively lower clay content. However, this hypothesis is still not verified. Therefore, MESDM is still subject to further developments based on new understandings from further experiments and validations against available observations (including MBC, and DOC) at different ecosystem sites with different soils and climates.

A AppendixThe Original Noah-MP Soil Carbon Model

The model represents fast soil organic carbon (SOC) pool turnover in a bulk layer using first-order decay kinetics and the accumulation of a slow SOC pool. The decay rate is dependent on vegetation types and is modified with soil temperature and moisture factors (Dickinson et al., 1998). A detailed description of the soil carbon model is based on the code of Noah-MP (https://www.jsg.utexas.edu/noah-mp/).

The decay rate of the fast SOC pool following first-order kinetics is described as follows: [Image Omitted. See PDF]where $$R$$ is the soil heterotrophic respiration (g C m⁻² s⁻¹), $${C}_{\text{fast}}$$ is the size of the bulk fast SOC pool within the root zone (g C m⁻²), $$\gamma $$ (=0.17 for grassland) is the microbial decay constant for the fast pool, which is dependent on vegetation type (μmol C [Kg C]⁻¹ s⁻¹), and $${f}_{T}$$ and $${f}_{W}$$ are scaling factors for the dependence of soil respiration on temperature and water saturation, respectively. The terms $${f}_{T}$$ and $${f}_{W}$$ are given as follows: [Image Omitted. See PDF] [Image Omitted. See PDF]where $${T}_{s}$$ is the soil temperature in the surface layer (K), $${Q}_{10}$$ (=2) is the factor by which the rate increases for every 10 K increase in temperature, and $$W$$ is the average relative soil saturation in the root zone.

The model assumes that the transformation rate from the fast pool to the slow pool is approximately 1/10 of $$R$$ and that all plant litter is added into the fast pool. The fast turnover pool decreases with decomposition and transformation losses and increases with the input of litter: [Image Omitted. See PDF]where $${C}_{\text{litter}}$$ is the input rate of plant litter (g C m⁻² s⁻¹). The slow pool increases with transformations from the fast pool: [Image Omitted. See PDF]

B AppendixThe O₂ and CO₂ Transport Models

We assume that gas transport in unsaturated soil can occur in the gas phase (Fang & Moncrieff, 1999). We consider that the gas concentration in the soil is governed by diffusive and convective transport as well as production and that the diffusive flux is calculated following Fick's law (Freijer & Leffelaar, 1996). Under the assumption of horizontal homogeneity, the one-dimensional vertical transport of O₂ is expressed through the mass balance equation (Fang & Moncrieff, 1999): [Image Omitted. See PDF]where $${O}_{g}$$ is the O₂ concentration in soil air (g O₂ m⁻³), $${\theta }_{g}$$ is the volumetric soil gas content (m³ m⁻³), $$t$$ is the time (s), $$Z$$ is the soil depth (m), $${D}_{\text{gO}}$$ is the effective diffusion coefficient (m² s⁻¹), $${q}_{g}$$ is the soil air flux (m s⁻¹), and $${R}_{h}$$ and $${R}_{a}$$ are the soil heterotrophic and autotrophic respiration rates, respectively (g C m⁻³ s⁻¹).

Using the Millington-Quirk model (Millington & Quirk, 1961), the O₂ effective diffusion coefficient $${D}_{\text{gO}}$$ can be estimated as follows: [Image Omitted. See PDF]where $${D}_{g}$$ is the O₂ diffusion coefficient in the atmosphere (m² s⁻¹). The effect of temperature and pressure on $${D}_{g}$$ is calculated from the following equation: [Image Omitted. See PDF]where $${D}_{g0}$$ is the O₂ diffusion coefficient in the standard atmosphere (1.39 × 10⁻⁵ m² s⁻¹) and $$P$$ is the atmospheric pressure (kPa) (Fang & Moncrieff, 1999).

Considering that the compressibility of soil air is negligible, we assume that changes in soil water volume must be immediately matched by corresponding changes in gas volume (Šimůnek & Suarez, 1993). Then, we calculate $${q}_{g}$$ at the soil depth, $$Z$$: [Image Omitted. See PDF]where $${q}_{w}$$ is the water flux at the soil depth $$Z$$ (m s⁻¹), $${Z}_{L}$$ is the depth of the lower soil boundary (m), and $$Q$$ is the root water uptake rate (m s⁻¹).

The upper boundary condition for Equation B1 is defined by the O₂ efflux at the soil surface and is defined as follows: [Image Omitted. See PDF]where $${q}_{O1}$$ is the O₂ flux at the soil surface (m s⁻¹), $${d}_{1}$$ is the thickness of the surface soil layer (m), and $${O}_{g1}$$ and $${O}_{a}$$ are the concentrations of O₂ in the surface soil layer and in the atmosphere, respectively (g O₂ m⁻³; $${O}_{a}$$ = 21% of the atmospheric density) The lower boundary condition for Equation B1 is defined as a zero-flux boundary condition.

One-dimensional CO₂ transport can be expressed by a mass balance equation: [Image Omitted. See PDF]where $${C}_{g}$$ is the CO₂ concentration in soil air (g C m⁻³) and $${D}_{\text{gc}}$$ is the CO₂ effective diffusion coefficient (m² s⁻¹). $${D}_{\text{gc}}$$ can be estimated in the same way as $${D}_{\text{gO}}$$ but necessitates the incorporation of the CO₂ diffusion coefficient in the standard atmosphere, $${D}_{g0}$$ (1.77 × 10⁻⁵ m² s⁻¹ for CO₂).

The upper boundary condition for Equation B6 is defined by CO₂ efflux at the soil surface and can be expressed as follows: [Image Omitted. See PDF]where $${q}_{C1}$$ is the CO₂ flux at the soil surface (m s⁻¹) and $${C}_{g1}$$ and $${C}_{a}$$ are the concentrations of CO₂ in the surface soil layer and in the atmosphere, respectively (g C m⁻³m⁻³; $${C}_{a}$$ = 0.035% of the atmospheric density). The lower boundary condition for Equation B6 is also a zero-flux boundary condition.

The Crank-Nicolson approach is used to solve the differential equations involved in the gas transport process.

Acknowledgments

This research was supported by the National Natural Science Foundation of China (Grant 41275090 and 41830967), the China Special Fund for Meteorological Research in the Public Interest (Grant GYHY201106028), and the NASA MAP Program (80NSSC17K0352). The authors thank Josh Schimel and other anonymous reviewers for their constructive and thorough comments that help improve the quality of the paper.

Data Availability Statement

The Santa Rita flux tower data (US-SRM) used in the paper is available online at the AmeriFlux website (https://ameriflux.lbl.gov/). Soil CO₂ efflux and concentration data and the FORTRAN code of new Noah-MP can be obtained online (http://data.lasg.ac.cn/zhangxia/). The code of Noah-MP is available online (https://www.jsg.utexas.edu/noah-mp/).