Model evaluation of different mechanisms driving freeze–thaw N2O emissions

Agriculture, Ecosystems and Environment 133 (2009) 196–207

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Model evaluation of different mechanisms driving freeze–thaw N2O emissions A.M.G. de Bruijn a, K. Butterbach-Bahl a,*, S. Blagodatsky a,b, R. Grote a a Karlsruhe Research Centre, Institute for Meteorology and Climate Research, Atmospheric Environmental Research (IMK-IFU), Kreuzeckbahnstr. 19, 82467 Garmisch-Partenkirchen, Germany b Institute of Physicochemical and Biological Problems in Soil Science, Russian Academy of Sciences, 142290 Pushchino, Moscow region, Russian Federation

A R T I C L E I N F O

A B S T R A C T

Article history: Received 12 August 2008 Received in revised form 10 February 2009 Accepted 27 April 2009 Available online 4 June 2009

N2O emissions from soil contribute significantly to global warming. Pulse emissions of N2O from soils during freeze-thawing were recently recognized as important atmospheric sources. In this modelling study we explore three different hypotheses for explaining freeze–thaw related N2O emissions: (1) soil frost or snow cover may reduce gas diffusion and create anaerobic conditions that stimulate N2O production via denitrification, (2) microbes that die of frost deliver easy decomposable organic carbon and nitrogen to the soil, which stimulates microbial growth and vigorous N2O production during freeze– thaw, and (3) the enzyme nitrous oxide reductase, which is responsible for the reduction of N2O to N2 during denitrification, is more sensitive to low temperatures than other enzymes, so that N2O becomes the dominating end-product of denitrification at low temperatures. These hypotheses were tested with a biogeochemical model that combines hydrology and physics calculations with a newly developed, parameter-poor biochemistry module. The model was first calibrated with field datasets on soil– atmosphere fluxes of N2O, NO and CO2 and soil NO3 and NH4 concentrations that were measured in a spruce forest in Southeast Germany in the years 1994–1997. Subsequently, additional model mechanisms were implemented that allow the model to describe the outlined mechanisms potentially driving freeze–thaw N2O fluxes. After each implementation the model was recalibrated. We were able to mimic dimension and timing of high N2O emissions when either one of the first two hypotheses were assumed, but found no confirmation for the third. The best model fit was achieved by combining hypothesis one and two, indicating that freeze–thaw N2O emissions are not mono-causal. ß 2009 Elsevier B.V. All rights reserved.

Keywords: N2O flux N2O modelling Freezing–thawing DNDC Nitrogen modelling PnET-N-DNDC Forest-DNDC

1. Introduction Nitrous oxide emissions from soils are estimated to contribute 6.1% to anthropogenic global warming (IPCC, 2007). Recent research has shown that winter emissions may significantly effect or even dominate the annual budgets of N2O emission from temperate and boreal soils (Ro¨ver et al., 1998; Papen and Butterbach-Bahl, 1999; Van Bochove et al., 2000; Butterbach-Bahl et al., 2002b; Mu¨ller et al., 2002; Groffman et al., 2006; Sharma et al., 2006; Holst et al., 2008). A multitude of physical, chemical and biological hypotheses have been proposed to explain the occurrence of low temperature related N2O emissions (Table 1). Physical explanations propose that gas diffusion rates become lower when liquids in soil pores are partially frozen (Bremner et al., 1980; Li et al., 2000). A slower diffusion of gases in frozen soils may result in an N2O peak while thawing, when N2O would accumulate in the soil and be emitted pulse wise when the soil thaws and soil pores widen again. It could also be an indirect cause as oxygen

* Corresponding author. Tel.: +49 8821 183136; fax: +49 8821 183294. E-mail address: [email protected] (K. Butterbach-Bahl). 0167-8809/$ – see front matter ß 2009 Elsevier B.V. All rights reserved. doi:10.1016/j.agee.2009.04.023

diffusion into the soil will be reduced if water starts to freeze, thereby expanding and narrowing soil pores. This will create anaerobiosis, with microbes using nitrogen oxides as alternative electron acceptors, i.e. favouring denitrification and, thus, N2O production via the denitrification pathway (Koponen et al., 2006; Mørkved et al., 2006). Another physical explanation lies with the assertion that freezing disrupts soil aggregates. This may mobilise dissolved organic carbon during thawing. Such enhanced substrate input has been hypothesized to stimulate microbial nitrogen conversions and associated N2O production (Groffman and Tiedje, 1989; Van Bochove et al., 2000; Sharma et al., 2006). A chemical mechanism has also been proposed to explain N2O pulse emissions during freeze–thaw. Christianson and Cho (1983) proposed that during freeze–thaw chemodenitrification increases, i.e. that microbial produced nitrite decomposes partially to N2O. Biological explanations are focusing on higher nitrogen availability for microbial metabolism during freeze–thaw. One mechanism would be that in winter plant uptake of nitrogen is low (Zak et al., 1990; Groffman et al., 1993), thus, leaving more N substrate for microbial N turnover. Microbial activity may still persist even when air temperature is below zero, since snow and upper soil layers buffer the temperature decrease and microbes can remain active in

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Table 1 Published hypotheses for freeze–thaw related N2O emissions from soils. Hypothesis

References

N2O diffusion rates are lower when water in soil pores is partially frozen Lower oxygen diffusion stimulates anaerobiosis and denitrification Freezing induces soil aggregate disruption and mobilises dissolved organic carbon Chemodenitrification increases with high nitrate concentration More nitrogen is available to microbial populations in winter because plant uptake is low Microbial activity continues because snow and upper soil layers buffer the temperature decrease and microbes remain active in deeper ground Microbes, dying of frost, deliver substrate to the soil which is decomposed progressively as temperature increases after the frost Fine root mortality increases due to frost and delivers substrate to the soil which is decomposed progressively as temperature increases after the frost Temperature sensitivity of N2O reductase will lead to lower N2 but increased N2O production during denitrification.

Bremner et al. (1980), Li et al. (2000)

deeper ground (Ro¨ver et al., 1998). Another argument for increased substrate availability during freeze–thaw is that microbes, dying of frost, deliver substrate to the soil which is decomposed progressively as temperature increases after the frost (Skogland et al., 1988; Ro¨ver et al., 1998; Mu¨ller et al., 2002; Sulkava and Huhta, 2003; Groffman et al., 2006; Koponen et al., 2006). This ambivalence, i.e. on the one hand active microbes and on the other hand dying microbes, is commonly explained by employing a concept of microsites and population diversity: High levels of microbial activity may also locally increase temperatures (Parkin, 1987) or low temperature resistant microbial populations remain active at some microsites. The decomposition of microbial tissues, produced by microbes that died of frost, could continue at these hotspots and produce N2O as a respiratory by-product (Parkin, 1987). Similarly, Fitzhugh et al. (2001) propose an increase in fine roots mortality as the main source of nitrogen loss during winter. Finally, it has also been hypothesized that changes in the activity of selected enzymes of the denitrification chain at low temperatures may be involved in freeze–thaw N2O pulse emissions. HoltanHartwig et al. (2002) indicate that the enzyme N2O reductase may be more sensitive to low temperatures than other enzymatic steps in the denitrification chain from NO3 to N2. This would minimize the reduction of N2O to N2 and may cause an increased production of N2O in the soil at low temperatures. There are objections to some of these hypotheses: (i) it is unlikely that chemodenitrifcation plays an important role during freeze–thaw because chemodenitrification is only of importance for soil N2O production at pH values lower than 3.5 (Mørkved et al., 2007), but freeze–thaw N2O pulses have a more general character, i.e. such pulses were also observed for soils with neutral pH values such as steppe soils (e.g. Holst et al., 2008). Moreover, significant chemodenitrification conversions presuppose high nitrite levels, but Ro¨ver et al. (1998) found that N2O is also released from soils when nitrite concentrations in the soils were low. Also the hypothesis that diffusion restrictions are leading to N2O accumulation in the soil matrix during winter, which is subsequently released during thawing has been challenged. Several authors have reported that N2O emission from soils are not seriously hampered by diffusion restrictions either by frost or snow pack (Duxbury et al., 1982; Sommerfeld et al., 1993; Kammann et al., 1998; Ro¨ver et al., 1998; Teepe et al., 2001). Moreover, also the view of increased substrate availability as driver for N2O pulses during winter can be seen critical at least as far as the role of fine roots is discussed. Fine root biomass generally has a low nitrogen content (1.0–2.0%), so that the increased availability of nitrogen due to the dying of fine roots in winter is assailable. Since high winter N2O

Li et al. (2000) Groffman and Tiedje (1989), Van Bochove et al. (2000), Sharma et al. (2006) Christianson and Cho (1983) Zak et al. (1990), Groffman et al. (1993) Ro¨ver et al. (1998)

Skogland et al. (1988), Mu¨ller et al. (2002), Ro¨ver et al. (1998), Groffman et al. (2006) Fitzhugh et al. (2001)

Holtan-Hartwig et al. (2002)

emission have also been observed (and for the first time) from unvegetated agricultural fields (Christensen and Tiedje, 1990), there should be additional factors in addition to fine root dying be involved to explain N2O pulses during freeze-thawing. Whereas many field, and laboratory studies have been published on the phenomenon of N2O winter emissions, comprehensive model studies to explain freeze–thaw N2O emissions are scarce, even though biogeochemical models are commonly understood as a useful tool to describe plant and microbial C and N turnover in ecosystems and soils. DNDC for example, relates nitrogen dynamics to agricultural practices (Li et al., 1992a,b). The agricultural version had been further developed towards a forest version by implementing a forest vegetation model (PnET, Aber and Federer, 1992) which was modified to consider also nitrogen uptake and release (Li et al., 2000). Forest-DNDC (previously PnET-N-DNDC) has been evaluated for N trace gas emissions from various forest ecosystems (Li et al., 2000; Stange et al., 2000; Butterbach-Bahl et al., 2001; Kiese et al., 2005; Kesik et al., 2005), even though it was not explicitly used for explaining freeze–thaw related N2O emissions. Norman et al. (2008) were able to mimic measured N2O winter emissions with a physics (diffusion and heat transfer) oriented biogeochemical model (CoupModel) that was adjusted to include microbiological process implementations from Forest-DNDC. However, the authors did not provide details what may have caused the peaks that were measured or simulated with their model. Forest-DNDC has recently been integrated into a new framework called MoBiLE (modular biosphere simulation environment) (Grote et al., submitted for publication). MoBiLE allows modellers to combine elements from different ecosystem models in order to apply the most appropriate selection for a specific task or to facilitate comparison of particular modules. In the framework of this study, an alternative soil biochemistry module for simulating microbial C and N turnover (DNDC2) was developed that interacts with the MoBiLE modelling environment. We used DNDC2 within the new mobile framework to evaluate different hypotheses. The aim was to single out those that may cause freeze–thaw related N2O emissions and excluded others. For this purpose, the new module was calibrated using measurements that were taken in the Ho¨glwald forest during a longer period (January 1994–December 1997). Consequently, model mechanisms were introduced that would be needed to enable the model to respond according to the mechanisms that are considered to explain N2O emission bursts during freeze-thawing. We excluded a priori: (a) N2O accumulates under snow or frozen soil and N2O is released during freeze–thaw (not in-line with observations); (b) the microsites hypothesis was not tested since a significant

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increase of temperature in microsites due to microbial activity was assumed to be unlikely; (c) a change in competition for nitrogen due to lowered nitrogen uptake by the vegetation is already included in the model and does not need to be tested separately. We finally tested three hypotheses: (1) frost and thawing reduces oxygen diffusion into the soil and thereby stimulates anaerobiosis and denitrification, (2) microbes, dying of frost, deliver substrate to the soil which is decomposed progressively as temperature increases after the frost, and (3) temperature sensitivity of the denitrification enzyme N2O reductase favours N2O as end-product of denitrification during freeze–thaw. The aim of our study was to test the most suitable hypothetic mechanism(s) in this model for their potential to predict timing, magnitude and dynamics of freeze–thaw emission peaks of N2O. 2. Materials and methods 2.1. Model description Simulating soil–atmosphere gas exchange with MoBiLE requires the selection of modules describing dynamics of soil chemistry

(including diffusion processes), soil temperature, moisture and vegetation. The vegetation module that was used goes back to the PnET model by Aber and Federer (1992), a modified version of which was used in the Forest-DNDC model (Li et al., 2000; Stange et al., 2000). The soil temperature and moisture modules are derived with small modifications from the Forest-DNDC model as well. The new soil chemistry module, DNDC2, simulates the decomposition of organic matter and explicitly considers nitrification and denitrification as N2O producing (denitrification also N2O consuming) processes. Thereby it also mimics microbial population dynamics involved in decomposition and inorganic N turnover (nitrification/denitrification). In DNDC2 as well as in the original Forest-DNDC anaerobic and aerobic processes such as debitrification and nitrification can occur simultaneously, the split between both is done via the anaerobic balloon (see also Li et al., 2000). The soil chemistry model is documented in Appendix A, a general overview is shown in Fig. 1. 2.1.1. Decomposition The model distinguishes three decomposition pools for plant tissues (types: lignin, cellulose type and solubles), and one stable humus pool (Appendix A: 2+3). Decomposition rates reduce with suboptimal temperature, moisture and soil pH (Appendix A: 83-.85). Litter residues are mobilised as dissolved organic nitrogen and dissolved organic carbon (Appendix A: 70, 73).

Fig. 1. Conceptual representation of soilchemistryDNDC2. The grey boxes represent pools of the soil biochemistry module. Numbered are (1) mineralisation, (2) nitrification and (3) denitrification. The nitrogen conversions are presented within the dotted box. These include assimilation of (4) nitrogen species and (5) dissolved organic carbon. The anaerobic balloon is a dynamic soil-depth specific volume fraction of aerobic versus anaerobic soil microsites, with nitrification only occurring at aerobic and denitrification only at anaerobic sites. Hypotheses 1–3 are the hypotheses used in the paper (1): stimulation of anaerobic growth and nitrogen conversion reaction, (2) enhanced availability of substrates due to dying microbes and (3) a pronounced sensitivity of N2O reductase enzymes.

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Table 2 Initial values for vegetation properties and soil parameters of the Ho¨glwald site as used for model initialisation. Data are either own measurements or were taken from published reports (Rothe, 1997; Rothe et al., 2002; Kreutzer, 1995; Kreutzer and Weiss, 1998). Data for soil properties are mean values of at least 10 replicated measurements. Tree species

Picea abies

Units

Number of samples

Stand height Average DBHa Stem volume Rooting depth

35.2 0.391 1312 1.2

m m m3 ha1 m

>10 >10 >10

Layer

Thickness (mm)

Soil density (kg dm3)

pH

Carbon content (g C (g soil)1)

Nitrogen content (g N (g soil)1)

1 2 3 4 5

72 100 100 100 100

0.13 1.02 1.34 1.59 1.59

3.3 3.36 3.99 3.76 3.76

0.325 0.02 0.018 0.018 0.018

0.009 0.0007 0.001 0.001 0.001

a

Diameter at breast height (=1.3 m).

2.1.2. Dynamics of microbial biomass and microbial growth A single microbial population divides into aerobic nitrifiers and anaerobic denitrifiers depending on the size of the anaerobic balloon (Appendix A: 87). Nitrifiers and denitrifiers have specific resources for growth and respiration (Appendix A: 75–81). Uptake of DOC and nitrogen species depends linearly on their respective concentrations and on the size of the microbial population, but the microbes reduce the fraction of carbon that is effectively assimilated into tissue when their C:N ratio is high (Appendix A:71, 86). A constant fraction of the microbial population dies each day (Appendix A: 72). 2.1.3. Ammonification and nitrification The microbes can consume DON, NH4, NO2, and NO3. In the predominantly aerobic soils we are simulating nitrification, whereas microorganisms that grow anaerobically, i.e. denitrifiers, use NO3 and other N-oxides as alternative electron acceptors. Nitrification is coupled to nitrogen assimilation by fixed fractions (YNx = fraction of unity, Appendix A: 75-81). Ammonification or nitrification fluxes can be calculated from the remaining (1  YNx) of the relevant nitrogen donor that is converted to the next level of oxidation (NO2, or NO3). Nitrification-related N2O and NO loss is calculated according to the hole-in-the-pipe concept, e.g. fixed fractions of the conversion flux from NH4 to NO2/NO3 are released as N2O and NO (Appendix A: 76, 77). 2.1.4. Denitrification The link between microbial population size and functional denitrification fraction is linear until a maximum is reached (Appendix A: 87). Anaerobic volume fraction is calculated according to the ‘‘average pore model’’ of Arah and Vinten (1995) as presented by Schurgers et al. (2006). The demand for electron acceptors from the nitrogen species NO3, NO2, NO and N2O is calculated from the quantity of DOC that is consumed for anaerobic microbial growth. Microbial preference of denitrifiers for nitrogen species used as electron acceptors generally depend on the electric charge and the number of free chemical bonds on the different species (Grant and Pattey, 2003) Denitrifiers are assumed to prefer nitrogen species that include a single nitrogen atom (NO3, NO2, and NO) over those that have two nitrogen atoms (N2O). This preference factor is combined with the concentrations of various relevant nitrogen species to calculate relative contributions of the electron acceptor species that are used to satisfy the electron acceptor demand of the denitrifiers while metabolizing DOC (Appendix A: 81).

2.1.5. Nitrogen deposition, leaching and gas diffusion Atmospheric deposition of nitrogen compounds generally consists of dry deposition, mostly of NH3 and NO2, and wet deposition, mostly of NO3 or NH4. In our model the N deposition is added to the upper soil layer with rainfall. From here it can be consumed by microorganisms or leached to deeper soil layers. NO3 and DOC move downward with a rate that depends on the concentration of the substances in a respective soil layer and the water flux between adjacent soil layers. The water flux is calculated in the hydrology module that is the same that is used in the original DNDC hydrology module (Li et al., 2000). The model relates the diffusion of gas species (gaseous nitrogen forms, oxygen, carbon dioxide) to the gradient of gas concentration in the soil profile. Effective diffusivity is calculated from water filled pores space according to the equations provided in Millington and Quirk (1961). This implementation is in accordance with the Forest-DNDC model (Li et al., 2000; Stange et al., 2000). 2.2. Site information and model initialisation The simulations are done for the spruce site of the Ho¨glwald Forest, a mature spruce plantation (approximately 100 years) located 40 km north-west of Munich, Germany. The Ho¨glwald is a long-term research site for which detailed information is available on trace gas fluxes and auxiliary parameters such as N deposition and leaching (Kreutzer, 1995; Rothe et al., 2002; Butterbach-Bahl et al., 2002b). Some characteristics of the site as used also for model initialisation are provided in Table 2. The Ho¨glwald Forest is embedded in an intensively used agricultural region. The site receives high loads of atmospheric N deposition (throughfall approximately 30 kg N ha1 yr1) with a ratio of NH4 to NO3 of 2:1 (Rothe et al., 2002). The climate is semi-continental with an annual average temperature of 8.5 8C. Long-term average annual precipitation is 888 mm (Kreutzer and Weiss, 1998), but varies between approximately 571 and 1054 mm (Kesik et al., 2005). Most precipitation is received as rain, but in winter snowfall occurs regularly. The soil is an acid hapludalf developed from Pleistocene loess over tertiary silty sand deposits (Kreutzer, 1995). The site has a very well developed litter layer (forest floor) of moder type, which is approximately 0.07 m thick. It is followed by an A-horizon that is approximately 0.05–0.10 m thick. Bulk soil density of the organic layer and the A-horizon is 0.11–0.29 and 1.03– 10.92 g cm3, respectively (Rothe, 1997). The C:N ratio of the organic layer and the A-horizon are 20–25 and 18–19,

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respectively, and further decreases with soil depth. The texture is 50–64% sand, 30–38% silt and 5–11% clay (Table 2, Butterbach-Bahl et al., 2002b). The site has been used for intensive field studies since 1982 (e.g. Butterbach-Bahl et al., 2002b; Kreutzer et al., 1991; Papen and Butterbach-Bahl, 1999). Air and soil temperatures (various depths) were continuously monitored for the period of July 1994 to January 1997. During the same period, ammonium and nitrate concentration in the Ol and Ah layer were measured weekly (Papen and Butterbach-Bahl, 1999). Automatic chamber measurements of soil CO2, N2O and NO emissions from the soil are available from November 1993 to May 1998 (ButterbachBahl et al., 2002b). The lower N2O fluxes are typically in the range of 0–5 g N ha1 d1, with N2O peak emissions of 15–90 g N ha1 d1 during a severe freeze-thawing event in late winter and early spring of 2006 (Papen and Butterbach-Bahl, 1999). NO fluxes are seasonal, with highest fluxes during the summer. Fluxes are in a range of 0–90 g N ha1 d1 (Gasche and Papen, 1999). 2.3. Evaluation of modelled and measured soil temperatures Adequate predictions of soil temperatures are a prerequisite for simulating the timing and severeness of freeze–thaw periods. Soil temperature was modelled with the DNDC soil physic module. This module calculates daily soil temperatures for a given soil layer (Li et al., 1992a). We compared on the one hand measured soil temperatures with modelled values but have had on the other hand a focus on the intensity and duration of frost periods. A similar analysis was carried out for the soil moisture. We compared measured and modelled water filled pore space, both with regard to magnitude and seasonality. 2.4. Model calibration and scenario analyses Model adjustments were introduced to account for the three hypotheses that were considered to explain freeze–thaw emissions individually and in combination. The model was recalibrated after each adjustment. 2.4.1. Hypothesis 1: Lower oxygen diffusion stimulates anaerobiosis and denitrification It is unclear whether the thaw peaks are caused by anaerobic conditions in the soil, and if they are, whether such anaerobic conditions are caused by soil ice or by a snow cover. Below such snow cover or layer of frozen soil, microbial activity would remain at temperatures around 0 8C. Even with low levels of activity, anaerobic conditions can stimulate the microbes to use nitrogen oxides as electron acceptor; hence relatively large quantities of denitrification products would be produced. We mimicked such behaviour by assuming that the fraction of the microbial community actively denitrifies increases at temperatures below 0 8C. In order to avoid far-reaching assumptions on the dynamics of such behaviour, we mimicked such behaviour by assuming that the fraction of the microbial community that actively denitrifies increases at temperatures below 0 8C. Such short-cut allows enough insight to discriminate between the selection of hypotheses but circumvents process and parameter uncertainties that would have to be dealt with if we were to implement a process based description of the effects of soil frost and snow cover on gas diffusion and, thus, anaerobic volume fraction. Defining by fd,frost, the incremented fraction of denitrifiers with freezing temperatures, we have: f d ¼ DF  Fanvf þ f d;frost

(1)

In Eq. (1), DF is the increment of the fraction of the microbial population that actively denitrifies, with an increment of the anaerobic volume fraction Fanvf and fd,frost further increments the fraction with freezing temperatures. The state variable fd,frost increases with a constant rate when the soil temperature at relevant soil depth is below 0.0 and decreases with the same rate when above:

d f d;frost ¼ Dfd when T sl < 0:0 dt

(2)

or

d f d;frost ¼ Dfd when T sl > 0:0 dt

(3)

where Tsl denotes a soil layer-specific temperature and Dfd is a cold related denitrifier response parameter (). When the soil temperature exceeds 0 8C, the denitrifier fraction decreases again to the level that is predicted from oxygen diffusion and consumption when temperatures are higher. For the sake of simplicity, the build-up and decrease of a frost-related denitrifier population fraction is assumed to proceed with an equal rate. 2.4.2. Hypothesis 2: Microbes, dying of frost, deliver dissolved organic carbon to the soil which drives growth when temperatures increase again Assumptions are minimal when we were to implement a qualitative response (only above or below 0 8C counts, not the number of below-zero degrees) and a linear increase of microbial deaths. Parameter Dfrost represents enhanced microbial death during the period of frost: 

dB dt



¼ ðD þ Dfrost Þ  B

(4)

decay

where D is the fraction () of the microbial population B (kg C) that dies each day, Dfrost denotes additional mortality that occurs in freezing conditions. Dfrost equals 0.0 when the modelled soil temperature exceeds 0.0 8C. The (additional) pool of dead microbial tissues C_litd decomposes like the other litter pools e.g. environmental response functions (temperature/moisture/pH: tdmdpd, in Appendix A: 83– 85) are the same as those for the litter decomposition. The balance of the pool of dead microbial tissue is then: 

dC litd dB ¼ dt dt

 decay

 t d  md  pd  K d

dC litd dt

(5)

Dfrost was tuned within a range of 0.0–0.1 g C g C1 d1. Kd, i.e. the decomposition constant for microbial tissues, was tuned within a range of 0.0 and 10.0 g C g C1 d1. 2.4.3. Hypothesis 3: N2O reductase is sensitive to lower temperatures A parameter dK N2 O reduces the potential conversion rate of N2O to N2, hence equation (Appendix A: 81) becomes:   dN 2 Oy dt den K DN  N2 O  28  ea (6) ¼ dK N2 O  K DN  ðNO3 þ NO2 þ NOÞ þ ð1:0  K DN Þ  N2 O where dK N2 O ¼ 1:0 when modelled soil temperature in a given depth is higher than zero. dK N2 O obtains its value from the program code that deals with the MCMC calibration procedure when the soil temperature at a relevant depth is higher than 0.0 8C. KDN is a dimensionless parameter that accounts for a preference that microbes have for molecules with a single N atom. ea is the demand for electron acceptors (moles) that is calculated from the

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respiration rate of the denitrifier fraction of the microbial population. It is tuned within a range of 0.0–0.1 g C g C1 d1. 2.4.4. Combinations of hypotheses It is likely that high winter N2O losses are not mono-causal. Additional to implementing and testing the three hypotheses separately, the model was therefore run with the combined hypotheses as well. For these combinations of hypothesis the same a-priori parameter ranges as well as additional parameters necessary to address the hypotheses (see above) were used to calibrate the model. 2.4.5. Model calibration A Bayesian approach based on Markov Chain Monte Carlo simulations was adopted to calibrate the model taking into

201

account uncertainties in the verification data (Brasswell et al., 2005; Zobitz et al., 2008). High model likelihood for a combination of objectives (model fit for measured CO2, N2O, NO emissions from the soil, NO3, NH4 concentrations) during a longer period (January 1994 to December 1997) was prioritized. A-priori parameter uncertainty ranges on potential decomposition rates (Ki) and responses to temperature (Q10, TOPT) were derived from incubation experiments (Berg et al., 1991; Henriksen and Breland, 1999, Appendix A: 83–85). Ranges for other parameters were derived from reported values whenever available. We used wide and uninformative ranges for potential indigestion rates of different elements (Appendix A 1.71, 1:74, 1:75). The model was first calibrated exposing all parameters that are involved in the biochemistry module. Consequently, the calibration was repeated after introducing the individual mechan-

Fig. 2. Simulations of soil temperatures on the left and soil moisture or snow cover on the right. (a–e) Compare modelled and measured soil temperatures Ts, from 1994 to 1997 and (f) is a close up of the period of the thaw-peaks. To the right, (g) is modelled snow cover (note that m refers to water equivalent). The model predicted that after the winter of 1995–1996, the last snow melted at April 18 (compare ‘snow melt’ in panels (f) and (g)), (h) is water filled pore space (vol%) in the humus layer and (i) is water filled pore space (vol%) in 10 cm mineral depth.

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isms, exposing a selection of parameters that are directly involved in the calculation of N2O efflux from the soil. The selection typically included nitrogen consumption rates, nitrogen and carbon assimilation efficiencies, and release fractions of N2O/NO from the nitrification flux, parameters on the denitrifier fraction and denitrifier preference for specific nitrogen species. 3. Results

are not uncommon since soil ammonium concentrations depend on various environmental factors such as clay absorption which are currently not included in DNDC2. The model performed better on the dynamics of NO3 concentrations (Table 3 and Fig. 3). The model also performed well on CO2 and reasonably well on NO, but it still missed the high N2O emissions during the winter period, which finally has led to a severe underestimation of N2O fluxes over the entire three years period. Corresponding explained variation ratios for the three years period were also minimal.

3.1. Evaluation of soil temperature and soil moisture The simulation period (1994–1997) includes four winters, in which soil temperatures were measured during two years. In every winter, there was a period of frost. The coldest air temperature was measured in 1997 (16.3 8C), whereas the freezing period was longest in the winter of 1996 (more than three months, with short periods of thaw). The model showed some weaknesses for predicting the temperature dynamics of the litter layers, but model performance in terms of R2 and root mean square error (RMSE) were much better for the lower soil layers. However, the model predicted the timing of the freezing periods correctly, even though the severity of the frost was underestimated (Table 3, Fig. 2a–f). The model underestimated the seasonal amplitude in moisture content for the forest floor and upper mineral soil. In agreement with measurements the water content during the freezing period decreased, but remained higher than the measurements. However, the low readings for measured soil moisture may be an artefact, since TDR probes were used, which do not recognize ice. Snow cover was estimated to be <0.08 m during the severe freezing period in winter 2006, with some patches close to stems even remaining uncovered by snow due to the rather dense canopy (LAI > 6). The model predicted snow covers up to 8 cm (water equivalent), which, thus, is reasonable for the site. The model predicted that the snow cover remains until the beginning of April 1996, which corresponds closely with the timing of the soil temperature increase after the frost. This further confirms that the model performs adequately on predicting snow cover (see Fig. 2a and g.). 3.2. Parameter calibration and scenario analyses 3.2.1. Default model The model performed well with regard to the magnitude of microbial N turnover and inorganic N production (NO3, NH4) in the soil, although it explained only a minimal fraction of the temporal variability in soil NH4 concentrations. However, such diversions

3.2.2. Hypothesis 1: Lower oxygen diffusion stimulates anaerobiosis and denitrification Model output for peak N2O emissions during freeze–thaw as well as for the emission during non-freeze–thaw periods agreed much better with the measurements than the default model (Fig. 3, Table 4). The estimated increment for the fraction of the microbial population that actively denitrifies was only minimal (6  105 g C(g C)1 d1, where the modelled default denitrifier fraction was approximately 1–2.4%). Soil nitrate and ammonium concentrations and modelled CO2 emissions for this scenario were similar to the standard model optimization, i.e. were in the range of observed concentrations. 3.2.3. Hypothesis 2: Microbes, dying of frost, deliver dissolved organic carbon to the soil which drives growth when temperatures increase again The mean emission value for the entire three years period with regard to N2O emissions was 3.73 and, thus, close to measured mean value of 3.88 g N ha1 d1. As for the parameterization for Hypothesis 1 also the parameter estimation for Hypothesis 2 resulted in low NO emissions during freezing and thawing. A possible explanation for this behaviour is that the emitted N2O in this scenario was derived by the further reduction of NO as produced by nitrification via denitrification. It is also worthwhile to mention that our model predicted freeze–thaw emissions for the winter of 1995. Though the timing of N2O peak in winter 1995 agreed with measurements, the simulated freeze– thaw N2O emissions lasted for a loner period than actually observed (Fig. 3d). 3.2.4. Hypothesis 3: N2O reductase is more sensitive to lower temperatures than other N-reductases When the normal procedure was employed to test this hypothesis, results were not as encouraging as for the first two hypotheses. Model performance criteria increased only minimally (Table 4), and likely are a mere consequence of adding the additional parameters. We also tuned several model parameters

Table 3 Root mean square error and explained variation for multiple model criteria. Model performances for soil temperature and water filled pore space were evaluated only. Modelled NH4 and NO3 concentrations in upper soil, emissions of CO2, N2O and NO resulted from the model, in which additional mechanisms that could explain freeze–thaw emissions were not taken into account. The model was calibrated for the period January 1, 1994 to December 31, 1996. Type of measurement (depth, unit)

RMSE

Mean measured

Mean simulated

R2

Forest floor temperature (8C) Soil temperature (0.05 m, 8C) Soil temperature (0.1 m, 8C) Soil temperature (0.15 m, 8C) Soil temperature (0.2 m, 8C) Water filled pore space (humus, %) Water filled pore space (10 cm mineral soil, %) NH4 (upper soil) NO3 (upper soil) CO2 emissions N2O emissions NO emissions

2.10 2.33 2.27 1.90 1.93 10.5 6.2

5.4 4.3 6.7 6.4 6.0 52.4 69.9

5.3 5.6 5.8 6.1 6.3 65.0 64.7

0.91 0.89 0.94 0.93 0.93 0.81 0.97

36.11 22.69 16.45 9.39 17.66

80.3 50.8 30.6 3.9 21.9

59.3 33.0 34.5 1.6 21.4

0.01 0.13 0.74 0.02 0.27

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203

Fig. 3. (a) Ammonium concentration in the upper soil 1994–1997, (b) nitrate concentration in the upper soil 1994–1997, (c) N2O emissions from the soil 1994–1997, (d) close up of the freeze–thaw event in spring 1996. Hypothesis 1: Lower oxygen diffusion stimulates anaerobiosis and denitrification, Hypothesis 2: Microbes, dying of frost, deliver dissolved organic carbon to the soil which drives growth when temperatures increase again, Hypothesis 3: N2O reductase is more sensitive to lower temperatures than other N-reductases. Please note that Hypothesis 1 and the default simulation cannot be identified in the figure because they are both very near to the axis.

Table 4 Coefficients of determination (R2) and root mean square error (RMSE) for model performances on N2O emissions (g N ha1 d1) from the soil. All criteria were derived for a longer time frame (January 1, 1994 to December 31, 1996).

Default Hypothesis 1 Hypothesis 2 Hypothesis 3 Hypotheses 1 and 2 Hypotheses 1 and 3 Hypotheses 2 and 3 Hypotheses 1–3

Mean measured

Mean simulated

R2

RMSE

3.88

1.61 4.74 3.73 2.10 2.92 3.31 4.31 2.95

0.02 0.74 0.32 0.03 0.81 0.67 0.36 0.76

9.39 5.14 7.80 9.73 3.83 5.31 7.32 4.73

irrespective of the general model performance to see what parameterizations would be needed to meet the quantity of freeze–thaw emissions of N2O. Extremely high default losses of N2 would be needed to support measured N2O emissions when N2O consumption would break down with low temperatures. Total annual N2 losses would sum up to 35 kg N ha1 yr1, which exceeds published estimates (Butterbach-Bahl et al., 2002c estimated 7–10 kg N2–N ha1 yr1) by at least a factor of three. Moreover, the resulting demand for nitrogen that is converted to N2 would decrease the nitrate concentrations far below measured levels. 3.2.5. Combinations of hypotheses The model fit improved from R2 = 0.74 (Hypothesis 1) to a R2 of 0.81 when a combination of Hypotheses 1 and 2 was assumed. The best model fit, however, was not found when all the hypotheses were assumed simultaneously, but instead when only the

decomposition hypothesis and stimulated denitrification hypothesis were assumed (Table 4 and Fig. 3). 4. Discussion Our results favour Hypotheses 1 and 2 as causes for freeze– thaw related N2O emissions. Some caution has to be taken here when judging on the relative contributions of these two factors when both hypotheses were applied, of course, because both hypotheses were implemented with a new parameter set. Hypothesis 1 states that N2O pulse emissions during freeze–thaw are mainly caused by limitations of O2 diffusion to the soil, which are resulting in increased anaerobiosis and stimulated denitrification activity in the soil. For Hypothesis 1 modelled and measured peak N2O emissions during freeze–thaw agreed best with regard to timing, magnitude and dynamic behaviour. A further confirmation comes from the fact that for this hypothesis, the model performed well on N2O emissions while it also simulated other outputs (NO3, NH4 concentrations, emissions of NO, CO2) within the uncertainty ranges that are associated with spatial variabilities that are commonly found for these features (e.g. Butterbach-Bahl et al., 2002a). The response of the fraction of microbes that actively denitrify corresponds well with estimates from an incubated soil: A recent paper estimates that two denitrifier genes (cnorBP and cnorBB, both belong to functional nitric oxide reductase cnorB) are present in 0.1–2.4% of the heterotrophic microbial population (Dandie et al., 2007), whereas in our model simulations the denitrifier fraction of the microbial population varies from 0.1–0.65%. However, caution should be taken when comparing the modelled denitrifier fraction with (laboratory)

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measurements, because the former is an aggregate of all functional types of microbes that are involved in nitrogen reductions. The importance of anaerobiosis for freeze–thaw N2O emissions was also highlighted by Koponen et al. (2006), who found that N2O emissions during such periods are a result of different factors, in particular anaerobic heterotrophic growth and associated N2O production by denitrification. Our model simulations are also inline with Mørkved et al. (2006) who found that N2O production during freeze–thaw was clearly related with soil oxygen concentration or, as in our model approach, with denitrifier activity. Furthermore, our model results support the statement of Mu¨ller et al. (2002) and Ro¨ver et al. (1998), who denied that N2O pulse emissions during freeze–thaw are due to precedent N2O accumulation in frozen soil. There are several differences between the diffusion of oxygen, and that of N2O. For example, the soil is an O2 sink while it is predominantly an N2O source. Moreover, O2 is a bulk gas whereas N2O is a trace gas. Finally, little is known on the quantitative relationship between soil O2 concentration, and extent of anaerobic zones and denitrification activity of microbes in the soil. We do not know whether denitrification increases linear with O2 levels or whether it responds to thresholds. The latter is most likely, since e.g. Ingwersen et al. (1999) as well as Parkin and Tiedje (1984) show experimental evidence, that denitrification in soils only becomes a dominating process for N2O production if O2 concentrations are <0.5%. Thus, at concentration close to these threshold values a further minimal decrease in oxygen level that is caused by lower diffusion rates could still significantly trigger anaerobic metabolism. Ro¨ver et al. (1998) mention high water filled pore spaces with associated anaerobiosis and N2O production as factor causing freeze–thaw N2O pulses, even though their paper emphasizes the importance of labile C as prerequisite for such emission events, which in our case is addressed by Hypothesis 2. The importance of high moisture contents as a driver for N2O freeze–thaw emissions is challenged by measurements and model results from the Ho¨glwald. Both results suggest that higher N2O emissions are not restricted to thawing conditions, but instead occur throughout the freezing period, i.e. during time periods when the free water (not frozen) is not exceptionally high (Fig. 2). This means that also for conditions with relatively low bulk soil moisture values, temperatures below zero will cause elevated N2O emissions if snow or ice cover sufficiently reduce O2 diffusion into the soil. This is in agreement with observations by Ro¨ver et al. (1998), who also observed that N2O emissions were already elevated at soil temperatures as low as 5 8C. A similar goodness-of-fit as for Hypothesis 1 was obtained when we assumed that dying microbes are a major driver for freeze–thaw associated N2O emissions, even though the shape of the freezethawing N2O peak differs from field observations (Fig. 3d). Thus, our model simulations confirm findings by several authors (Skogland et al., 1988; Ro¨ver et al., 1998; Papen and Butterbach-Bahl, 1999; Mu¨ller et al., 2002; Groffman et al., 2006; Koponen et al., 2006), who also showed that dying of microbial biomass during frost provided additional substrate for decomposition and that this flush in substrate is triggering freeze–thaw N2O emissions. Skogland et al. (1988) motivate their findings from simple kinetics and explain the respiration response as a consequence of substrate input when population density is relatively high. Aerobic decomposition and related nitrification, however, would imply high levels of NO production. Neither in the Ho¨gwald forest (Gasche and Papen, 1999) nor in boreal organic soils (Koponen et al., 2006) were higher levels of NO emissions from soils measured during freeze thaw events. A similar finding applies to our simulations. When, as in our model, denitrification is proposed as a major source of thawing-related N2O production, NO consumption

by denitrification is high so that a maximum in NO emission can only be seen shortly after thawing. This proposed NO consumption by denitrification as a regulating factor of NO emission is supported by the Ho¨glwald dataset (Gasche and Papen, 1999) and our model runs. In contrast to Skogland et al. (1988) who found enhanced microbial respiration rates only after the onset of soil thawing, our simulations as well as the field measurements show that N2O emissions were enhanced already during the entire period of frost. Our model simulations suggest that the temperature sensitivity of N2O reductase may only account for a minimum fraction of elevated N2O emissions during freeze–thaw. An explanation that refers to such a mechanism as a primary driver of the process is challenged by the notion that the potential loss of N2O with a malfunctioning of N2O reductase, primarily depends on the total N2 + N2O loss. In our model tests the annual N2 losses required to allow a malfunctioning of the N2O reductase enzyme at low soil temperatures to explain freeze– thaw related N2O emissions would equal 35 kg N2 ha1 yr1, This exceeds the estimate by Butterbach-Bahl et al. (2002c) for the Ho¨glwald Forest, which was based on a soil core incubation method, by at least a factor of four. Furthermore, such a mechanism would require a significant accumulation of NO3 during the freezing period, which has not been observed (Papen and Butterbach-Bahl, 1999). If Hypotheses 1 and 2 were combined, i.e. O2 diffusion restrictions – simulated here as an increase in denitrifier fraction – plus accumulation of easily degradable substrate due to the dying of microbes, we were able to further increase the predicting capability of our model simulations (Table 4). This means, that freeze–thaw N2O emissions may most likely be due to the combination of increased anaerobiosis favouring denitrification combined with a flush of substrate during freeze–thaw. This is in-line with the conclusions drawn by Koponen et al. (2006) and their work on freeze–thaw related N2O emissions from boreal organic soils. 5. Conclusions We have found indications that frost and thawing reduces oxygen diffusion into the soil and thereby stimulates anaerobiosis and denitrification. These findings confirm Li et al. (2000). It is, however, unlikely that the phenomenon is caused exclusively by higher denitrification rates. A secondary factor of importance could be that microbes, dying of frost, deliver substrate to the soil which is decomposed progressively as temperature increases after the frost. These findings confirm Skogland et al. (1988), Papen and Butterbach-Bahl (1999), Mu¨ller et al. (2002), Ro¨ver et al. (1998) as well as Groffman et al. (2006). We found that a retarded or damped anoxic conversion of N2O to N2 was unlikely as an explanation of freeze–thaw emissions of N2O. In view of the nitrate concentrations that are low while the cold endures, these substrates, however, would have to be used as electron donors instantaneously. Acknowledgements This work is a contribution to the EU funded Integration Project NitroEurope. Further thanks go to Peter A. Leffelaar and Guy Schurgers who have made available their models on anaerobic volume fraction (Schurgers et al., 2006) and denitrification (Leffelaar and Wessel, 1988) and gave several helpful comments and suggestions. The authors would like to thank the European Commission funded research project NitroEurope IP (contract 017841), COST Action 729 and the ESF Nitrogen in Europe (NinE) programme for supporting the research and collaboration underpinning the results presented in this paper.

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205

Appendix A. Parameters and module description of DNDC2 Reference numbers

Notations (states)

1 2 3 4 5 6 7 8 9 10 11 12

B C_litl C_hum C_microl DOC DON NH4 NO N2O NO2 NO3 Tsl

13 14 15 16 17 18 19 20 21 22

23 24 25 26 27

Microbial biomass Litter pool (1 = lignin, 2 = cellulose, 3 = solutes) Humus pool Microbial pool (1 = aerobic nitrifiers, 2 = anaerobic denitrifiers) Dissolved organic carbon Soil dissolved organic nitrogen content Soil ammonium content Soil Nitrogen oxide content Soil nitrous oxide contents Soil nitrite content Soil nitrate content Soil layer temperature

gC gC gC

mol – –

ydoc wf

Electron acceptor demand Denitrifier fraction Moisture correction factor Correction factor for soil pH Temperature correction factor Air filled soil porosity Anaerobic volume fraction Total soil porosity Carbon assimilation efficiency Soil water flux

Subscripts ass resp den nitr leach

Assimilation Respiration Denitrification Nitrification Leaching

Notations (intermediates) ea fd md pi

td ua Fanvf utot

Notations (model parameters) C dYDOC D DF FN FNO FDMAX FH G h K1 K3 K2 KH KDON K NH4 K NO2 K NO3 KDOC KDN Q10

28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54

TOPT YDON Y NH4 Y NO2

55

dC lit ¼ dt

56 57 58 59 60 61 62 63 64

uopt uS

Differential equations 3      X dC litl dC litl  dt dt lit dec i¼1     dC hum ¼ dC hum  dC dhum dt dt t hum dec   dDOC dDOC dDOC ¼ dDOC  dt dt dec dt assþresp  dt leach     dB ¼ dB dB dt dt growth  dt decay   dDON dDON ¼ dDON dt dt dec  dt assþresp     dNH4 dNH4 dDON dt ¼ dt resp  dt assþresp   dNO dNO dNO ¼ dNO dt dt nitr  dt den  dt diff         dN2 O dN 2 O dN 2 O dN2 O dNO dt ¼ dt nitr þ dt den  dt den  dt diff       dNO2 dNO2 dNO2 dNO2 dt ¼ dt nitr  dt nitrþass  dt den       dNO3 dNO3 dNO3 dNO3 ¼   dt dt dt dt nitr

den

leach

gC gN gN gN gN gC 8C

– – – – g C g C1 d1

Humification flux Shape parameter for moisture dependency Heterotrophic microbial decay rate Shape parameter for anaerobiosis dependent denitrifier fraction N-loss during nitrification (hole-in-the-pipe) N-loss during nitrification as N2O (hole-in-the-pipe) Maximum denitrifier fraction Detritus fraction that turns over to humus Nitrogen gas species or CO2 content in soil layer Soil layer thickness Mineralisation rate of lignin Mineralisation rate of solutes Mineralisation rate of cellulose Mineralisation rate of humus Potential DON consumption Potential NH4 consumption Potential NO2 consumption Potential NO3 consumption Potential DOC consumption Denitrifier preference to single-N molecules Decomposition response to a 10 8C increase in temperature Optimum water filled pore space Shape parameter Optimum decomposition temperature Efficiency of DON assimilation Efficiency of NH4 assimilation Efficiency of NO2 assimilation

g C g C1 – g B g B1 d1 – – – – – g C or g N m2 m g C g C1 g C g C1 g C g C1 g C g C1 g N g B1 d1 g N g B1 d1 g N g B1 d1 g N g B1 d1 g C g B1 d1 – g C g C1 d1 – – 8C – – –

Balance of litter pool l (1 = solutes, 2 = cellulose, 3 = lignin)

g C d1

Balance of the humus pool

g C d1

Dissolved organic carbon balance

g C d1

Microbial biomass balance

g C d1

Dissolved organic nitrogen balance

g N d1

Ammonium balance

g N d1

Nitrous oxide balance

g N d1

Dinitrogen oxide balance

g N d1

Nitrite balance

g N d1

Nitrate balance

g N d1

206

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Appendix A (Continued ) Reference numbers

Notations (states)

65

dDOC dCO2 dt ¼ dt resp

66

Fluxes 

dC litl ¼ dt dec

67

dC

68

dC



69

dDOC

70

dDOC

hum

dt

hum

 hum

dt

dec

dt dt

72

dB

73

dDON

74

dDON

77 78 79 80 81 82

¼ t d  md  pd  K H  C hum

¼

dec

dB

76

¼CDB

assþresp

71

75

t d  md  pd  K l  C litl



¼ ð f d  K c  DOC  BÞ=yDOC

3  X dC

litl



dt

dec

l¼1

  þ dC dhum t dec



dDOC dt ass ¼ dt ass  yDOC

dt

dec

dt



assþresp

   

nitr

g C d1

Microbial decay

g C d1

Humification

g C d1

Humus decomposition

g C d1

DOC consumption

g C d1

DOC production by decomposition

g C d1 g C d1

DON production by decomposition

g N d1

¼ ðK DON  DON  ð1:0  f d Þ  BÞ=Y DON

DON consumption by assimilation and ammonification

g N d1

NH4 consumption

g N d1

Nitrification-N allocated to NO

g N d1

Nitrification-N allocated to N2O

g N d1

Nitrification-N allocated to NO2

g N d1

NO3 production through nitrification

g N d1

Assimilative NO2 consumption and NO2 oxidation

g N d1

Denitrification

g N d1

Upward diffusion

g N d1

Temperature reduction

–

Soil moisture reduction

–

dNH4 ¼ ðK NH4  NH4  ð1:0  f d Þ  BÞ=Y NH4 dt nitrþass dt

Litter decomposition

Microbial growth 



dNO 

¼

g C d1

  dC lit3 =CNL þ dhum dt dt dec =CNhum dec

dt decay ¼ D  B



Carbon dioxide production

¼ F N  F NO 





dNH4 dt nitr



dN2 O dt nitr ¼ F N  ð1:0  F NO Þ 



dNO2 dt nitrþass ¼ ð1:0  F N Þ 







dNH4 dt nitr



dNH4 =Y NO2 dt nitr



dNO3 dt nitr ¼ K NO2  NO2  ð1:0  f d Þ  B



dNO2 dt nitrþass ¼ ðK NO2  NO2  ð1:0  f d Þ  BÞ=Y NO2



dNx Oy K Nx Oy ¼ K ðNO þNO DN  14  x  ea dt DN 3 2 þNOÞþð1:0K DN ÞN2 O den

  dNx O or dCO2 ¼ dt dt

f ðGsl Gsl1 Þ h2

Additional equations 83

ðTT OPT =10Þ t d ¼ Q10;d

84

md ¼

85

pi ¼ 1:0  eðpH6:3=1:5Þ

Soil pH reduction

–

86

ydoc ¼ 1:0edYDOC cnb

Carbon assimilation efficiency

g C g C1

87

Denitrifier fraction

–

Electron acceptor demand

mol e

89

f d ¼ MinðFDMAX ; DF  Fanvf Þ   4 ea ¼ 12  ddBt ass   dNO3 ¼ wf  NO3 dt

Leaching

g N d1

90

f ¼ ua

 2  uua tot

Effective diffusivity

m d1

91 92 93

CNL (not shown) CNH (not shown) CNB (not shown)

Lignin C:N ratio Humus C:N ratio Microbial C:N ratio

g C g N1 g C g N1 g C g N1

88

1:0 ðfu opt ÞuS 1:0þe

leach

1:33

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