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344 DOI: 10.1002/jpln.200700075 J. Plant Nutr. Sci. 2008, 171, 344–354 across scales: The importance of a model–data integration framework for data interpretation§ Markus Reichstein1* and Christian Beer1 1 Max-Planck Institute for Biogeochemistry, Biogeochemical Model-Data Integration Group, Hans-Knöll-Str. 10, 07745 Jena, Germany

Abstract Soil respiration represents the second largest CO2 flux of the terrestrial biosphere and amounts 10 times higher than the current rate of fossil-fuel combustion. Thus, even a small change in soil respiration could significantly intensify—or mitigate—current atmospheric increases of CO2, with potential feedbacks to climate change. Consequently, to understand future dynamics of the earth system, it is mandatory to precisely understand the response of soil respiration to chan- ging environmental factors. Among those changing factors, temperature is the one with clearest and most certain future trend. The relationship of soil respiration to environmental factors and particular temperature has been tackled at a variety of scales—from laboratory via field scale to global, with each of the approaches having its particular problems, where results from different scales are sometimes contradictory. Here, we give an overview of modeling approaches to soil respiration, discuss the dependencies of soil respiration on various environmental factors, and summarize the most important pitfalls to consider when analyzing soil respiration at the respec- tive scale. We then introduce a model–data synthesis framework that should be able to reconcile and finally integrate apparently contradictory results from the various scales.

Key words: soil respiration / modeling / upscaling / Bayesian / temperature dependence

Accepted January 26, 2008

1 Introduction With globally 68–120 Pg C y–1 soil respiration represents the In this study, methods and problems analyzing soil-respira- second largest C flux between and the atmo- tion data from different scales are reviewed and jointly inter- sphere (Schimel et al., 1996). This is more than 10 times the preted with emphasis on the temperature and moisture de- current rate of fossil-fuel combustion and indicates that each pendence of soil respiration. The application of an year approx. 10% of the atmosphere’s CO2 cycles through model–data integration framework which is developed in a the soil. Thus, even a small change in soil respiration could cascade from fine scale to landscape scale, and parameter- significantly intensify—or mitigate—current atmospheric ized by using observations across these scales, is proposed increases of CO2, with potential feedbacks to climate change. to provide additional insights into the factors controlling tem- Despite this global significance as well as considerable scien- poral and across-ecosystem variability of soil respiration and tific commitment to its study over the last decades, there is C content. still limited understanding of the factors controlling temporal and across-ecosystem variability of soil respiration. 2 Environmental factors controlling soil This understanding is largely hampered by the fact that stud- respiration ies are often conducted and compared at different temporal and spatial scales that are not compatible. Since particularly 2.1 Abiotic factors in large-scale studies factors influencing soil respiration often correlate with each other, responses of soil respiration to Temperature is virtually influencing all biological and physico- those factors are confounded by other factors, and only chemical processes. This has been empirically observed in apparent relationships are obtained. the 19th century (van’t Hoff, 1898) and later formalized by

* Correspondence: Dr. M. Reichstein; e-mail: [email protected] § Paper presented at the Workshop “Upscaling – Soil organisms and soil ecological processes up to the landscape scale”, February 23–24, 2006 at the University of Vechta, Germany. The workshop was organized by the Working Groups of the German Society (DBG) and the Ecological Society of Germany, Austria, and Switzerland (GfÖ), convenor Gabriele Broll and co-con- venors Volkmar Wolters and Anton Hartmann.

 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim www.plant-soil.com J. Plant Nutr. Soil Sci. 2008, 171, 344–354 Soil respiration across scales 345

Arrhenius (1889). Not surprisingly, temperature has also perature. Since act in a certain temperature inter- been the most obvious and most often studied factor influen- val, all biological processes exhibit optimum temperatures. cing soil respiration, one of the first studies dating back to the Hence, the optimum function (Kirschbaum, 1995) may be 1920s (Waksman and Gerretsen, 1931). All studies confirm a considered as the most appropriate description. However, nonlinear positive direct relationship between temperature soil temperatures rarely reach such high values, so that with- and soil respiration. A number of shapes have been pro- in the normal range of temperatures, the monotonic exponen- posed, but the most commonly used are reviewed by Kätterer tial function may be as valid. et al. (1998), Kirschbaum (1995) as well as by Lloyd and Tay- lor (1994). The simplest, but theoretically not justified function The effect of status on soil respiration has been de- is the so-called exponential Q10 relationship (Tab. 1), where scribed empirically via absolute or relative measures of volu- the parameter Q10 is the factor by which soil respiration in- metric water content and soil water potential as reviewed by creases with a 10°C temperature increase. The Arrhenius Rodrigo et al. (1997) (see examples in Tab. 2). It is usually function is theoretically justified from first physicochemical assumed, that both very low and very high water contents principles of the underlying biochemical reactions and pre- reduce soil respiration, via direct inhibition of biological activ- dicts an increasing Q10 towards lower temperatures. How- ity or inhibition of O2 diffusion, respectively. The relationship ever, the validity of a simple transfer from physicochemical between soil water status and soil-respiratory processes is reactions to complex processes controlling soil respiration complex, since many individual processes vary with soil has not been proved yet. Instead, more flexible exponential water content, in particular gas and solute diffusion, relationships have been derived from empirical field data, activities, and growth and mortality of (Kill- which imply an even stronger variation of the Q10 with tem- ham, 1994; Marshall and Holmes, 1988). Soil water potential

Table 1: Typical functions used for describing soil respiration in relation to temperature.

Author Function Background Properties dfa

†‰ŠÀ = van't Hoff (1898) †ˆ Á T Tref 10 emprical always above 0 2 f T a Q10

2 Ratkowsky et al. (1982) f T †ˆa Á T À Tmin† empirical studies on zero respiration at T = Tmin 2 microbial growth

ÀE0= RÁT † Arrhenius (1989) f T †ˆa Á e physical chemistry always >0, very similar to Q10, 2

ÀEa = T ÀTmin† Lloyd and Taylor (1994) f T †ˆa Á e Arrhenius + study on zero respiration at T = Tmin,no 3 field respiration optimum

Á À : = † O'Connell (1990); f T †ˆa Á eb T 1 0 5T Topt empirical studies on optimum function 3 Kirschbaum (1995) soil respiration in lab a degrees of freedom (i.e., number of free parameters)

Table 2: Typical model formulations used for soil-drought effects on soil respiration. Formulationa References

Dependency on volumetric  f †ˆa Á  ‡ b (plain linear) Stanford and Epstein (1974)

À f †ˆa Á b (scaled linear) Myers et al. (1982) opt Àb

 f †ˆ (hyperbolic) Bunnell et al. (1977) a1‡

Dependency on soil water potential É É†ˆ Á log ÀɆ‡ f m 10 c Sommers et al. (1981); Orchard and Cook (1983); Andrén and Paustian log ÀɆÀlog ÀÉ † (log-linear) (1987) Ɇˆ 10 10 min f log ÀÉ †Àlog ÀÉ † 10 opt 10 min f Ɇˆa Á ebÁÉ (exponential) Davidson et al. (1998)

Dependency on proportion of water-holding capacity P À †‡ À †2† f P†ˆe a P Pref b P Pref (exponential) Howard and Howard (1993)

a symbols a, b, hopt, hb, a1, m, c, Wmin, Wopt, Pref are model parameters determining the shape and scale of the functions.

 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim www.plant-soil.com 346 Reichstein, Beer J. Plant Nutr. Soil Sci. 2008, 171, 344–354 has often been considered the physiologically more appropri- optimally under neutral conditions while fungi prefer slightly ate predictor of activities in soil, because it expresses the acidic soil pH. A recent study has shown that such optimum actual availability of water independent of texture (Davidson curve can be found through analysis of field data of respira- et al., 1998; Miller and Johnson, 1964). However, plausible tion (Reth et al., 2005), although confounding factors have to arguments for soil water content as a predictor have also be considered. been presented, based on the reasoning that the number and extent of microenvironments where microbial activity may Also in the temporal domain, processes from various time- take place is a function of the volume of the water in the soil scales overlap and superimpose on the resulting soil biologi- (Fang and Moncrieff, 1999; Orchard and Cook, 1983). cal activity and soil respiration (Fig. 1). Consequently, a cur- Furthermore, and O2 diffusion seem to be better de- rently observed soil respiration can be the result of processes scribed as dependent on soil water content (Skopp et al., that have occurred a long time ago. A typical example for this 1990). A practical advantage of water content as a predictor would be the unusually high and persisting soil respiration is that it is more readily measured in the field than water from crop fields that have been established on previous - potential, but the criticism remains that water content is not land by hydrological regulation and aeration. Another relevant comparable among different classes. A possible example is the effect that after a long soil drying and subse- way to partly overcome this problem is to express soil water quent rewetting, soil-respiration rates often exceed rates content as a proportion of water-holding (field) capacity or under well-watered conditions before the drying. This so- available water, because then the effect of texture on water called Birch effect has been first observed in the laboratory availability is included to some extent. and is usually explained by the rapid mineralization of microbes that died during the drying, a dynamic effect (Birch, Obviously, there are indirect effects of drought on soil respira- 1958). Recently this effect has been found being of impor- tion, e.g., the impact on soil macrofauna which may retreat tance also for ecosystem C dynamics (Borken et al., 2003; into deep layers and/or fall dormant under drought. Although Xu and Baldocchi, 2004). The scheme in Fig. 1 also eluci- macrofauna assimilates <10% of C, it acts as important cata- dates that the type of model developed to describe soil lyzer by cracking larger structures and increasing the reaction respiration (i.e., the processes included) must be dependent surface area. Also, rewetting events often increase soil on the temporal extent that needs to be covered by the appli- respiration by large amounts, which can only be explained by cation of the model. remineralization of dead or by desorption processes, which make labile substrate available to microbes (Orchard and Cook, 1983). While the temperature dependency of soil 2.2 Biotic factors respiration has been analyzed for different compartments Given that soil respiration is by >90% a biological process, it (roots, litter, mineral soil) with quite different observed is conceptually evident that biotic factors are important deter- responses (Anderson, 1991; Liski et al., 1999), no such minants of soil respiration. Roots as well as microorganisms efforts have been undertaken with respect to drought effects. eventually depend on the carbon supply that is assimilated by the green and enters the soil via phloem transport Other abiotic factors have been much less systematically stu- to the root, root exudation, and incorporation of dead plant died than soil water availability and soil temperature, but material into the soil (litter fall). The proportion of root respira- include soil acidity, O2 and nutrient availability. Oxygen can tion has been shown to vary usually between 30% and 70%. be a limiting factor a of soil respiration in water-logged Extreme values of 10% and 90% have been reported, but or in aggregates after rain events, that cause anaerobic con- those numbers may be subject to extreme conditions and ditions. The response of soil respiration to soil acidity is methodological problems. Global analysis of soil-respiration thought to be an optimum function, where bacteria operate data sets has clearly shown, that soil respiration is strongly

sSOM formatiom

Succession of vegetation

Varying litter pools

Root, microbial macro-fauna dyna.

Soil heat dynamics, unsaturated flow

Diffusion, of water

0123456789101112 Figure 1: Dominant temporal scales of factors and processes influencing soil respiration. (sSOM = stabile Log(Timescale [s]) minute hour day month year soil ).

 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim www.plant-soil.com J. Plant Nutr. Soil Sci. 2008, 171, 344–354 Soil respiration across scales 347 correlated with net primary productivity (Janssens et al., where Ii is the input to the pool I, Ci is the pool size (e.g.,kg –2 2001; Raich and Schlesinger, 1992; Raich and Tufekcioglu, m ), and ki is the first-order rate constant (cf., 2000). Fig. 2). Labile pools with high decomposition rates are , alcohols, and , while , ligno-cellulose, waxes, Macrofauna cracks large structures, thereby making avail- and lignin are considered more stabile components. Depen- able substrate for microorganisms and increasing the surface dences of ki on temperature (Tab. 1) and moisture (Tab. 2) area for biochemical reactions. Thus, macrofauna importantly are mostly assumed to be multiplicative although this must acts as catalyzer for the decomposition of soil organic mate- be questioned (Borken et al., 1999; Carlyle and Than, 1988; rial (SOM). Reichstein et al., 2003a) since the relationship between soil water status and soil-respiratory processes is complex (see above). Humification is modeled as transition from a more 3 Modeling approaches labile to a more stabile pool. This concept goes back to Jenny (1941) and Meentemeyer (1978). Soil respiration—defined as the CO2 efflux from the soil sur- face—originates from the metabolic activity of roots (auto- trophic respiration), microorganisms (bacteria, actinomy- cetes, fungi), and soil meso- and macrofauna (heterotrophic respiration). Only under certain circumstances (carbonate i soils), significant amounts of CO2 can abiotically evolve through weathering of carbonates (e.g., CaCO ). While for 3 r·k ·(1-h)C modeling carbon assimilations by plants, the leaf is easily Young 1 1 carbon identified as the functional unit with clear boundaries and a C1 well-known organization of tissues and a general biochemis- try (Calvin-Cycle), soil processes occur very heterogeneously r·k ·h·C 1 1 CO without a single functional unit. Instead, a number of organ- 2 isms and enzymes are decomposing a large variety of chemi- cal substances. Moreover, while virtually all higher plants are r·k2·C2 described as species and a large number of plant species of var- Old carbon ious functional types have been studied extensively, not even C2 10% of soil microbes are described at all. Consequently, for modeling plant productivity, species-oriented and reductionistic approaches have been successful, while soil respiration is Figure 2: Simplest useful soil organic matter–decomposition model often modeled as a whole (holistic approach), and soil pro- (two pools, five parameters), the Introductory Carbon Balance cesses are more related to the substances that are decom- Model—ICBM (Andrén and Kätterer, 1997). posed rather than to the function of decomposing species.

Despite the obvious importance of biological control of soil The structure of current soil respiration models is oversimpli- respiration, empirical models have often not included biotic fied in several ways. First of all, biotic constraints on soil factors but focused mainly on the abiotic controls. Even for respiration, environmental effects on the population dynamics global and interannual variation, models are developed that of macrofauna and microbes, remineralization of dead bio- predict soil respiration solely from climate variables (Raich mass, and drought-influenced seasonality of root-exudation and Potter, 1995; Raich et al., 2002). The hypothesis behind and growth respiration are mostly neglected. In addition, the these climatically driven models is that vegetation productivity quite pronounced vertical differentiation in soils is largely and climate are correlated and their effect on soil respiration neglected. For instance, the decomposition rate of SOM in cannot be disentangled. However, Reichstein et al. (2003a) different depths depends on the temperature and moisture in showed that it is possible and necessary to separate climatic those depths (see below). The soil also is a horizontally very and biological effects on soil respiration, since their biologi- heterogeneous system, which is constantly modified and cally driven model explained more than 6-fold more site-to- organized by organismic activity. This leads to a concentra- site variance of soil respiration data than a climate-driven tion of the activity into few areas. Hence, one has to consider model. that the environmental factors that prevail in those areas are important for the soil activity and respiration, and not neces- Mechanistic models generally rely on a few common para- sarily average conditions in the soil. In current soil-respiration digms when modeling soil respiration. Root respiration is models, a number of processes (e.g., or microbial assumed—as for other plant tissues—to be the sum of growth dynamics) are not explicitly considered, nor a direct growth and maintenance respiration, according to the link (other than litterfall) from assimilation to belowground 30 year–old so-called Penning-de-Vries paradigm (Amthor, processes. Recent girdling experiments seem to indicate that 2000). Heterotrophic respiration is usually modeled as the current models underestimate the importance of the interac- decomposition of 2–8 SOM pools with different turnover tions between aboveground and belowground processes times. According to this approach, each pool decomposes (Högberg et al., 2001; Subke et al., 2004). Biologically with a first-order kinetic, analogue to nuclear decay: focused, food-web-based models of soil respiration have been developed, but did not achieve much general attention dCi ˆ I À k C , (Hunt, 1977; Hunt et al., 1977; Smith et al., 1998). dt i i i

 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim www.plant-soil.com 348 Reichstein, Beer J. Plant Nutr. Soil Sci. 2008, 171, 344–354

4 Extracting the response of soil respiration ature treatments. In the literature, it is very often not reported to environmental factors when and how the Q10 was derived, e.g., the decent scatter of Q10s in the review by Kirschbaum (1995), may have been While a general description of the response of soil respiration caused by these spurious changes in Q10. to environmental factors (see above) seems quite straightfor- ward, there are a number of complications that occur when a formal modeling of soil respiration, e.g., in response to tem- As a consequence, it is dangerous to derive the Q10 of C perature, is sought. These complications arise mainly from mineralization from the respiration rates at only one arbitrary misunderstandings about what “the response of soil respira- incubation time, because then the temperature effect is con- tion to temperature” actually is and from different interpreta- fused with the incubation-time effect. There are three ways to tions at different scales. The largest misunderstanding may solve this problem: (1) to calculate the Q10 values from only occur between field ecologists and mechanistic modelers of the respiration rates at the beginning of the incubation (e.g., soil respiration. The former would define the response of soil Winkler et al., 1996), because the composition of the samples respiration to temperature basically from the scatter between is still unaltered, (2) to use the respiration rates at a very late incubation time (e.g., Ross and Cairns, 1978), when the light observed soil CO2 efflux and measured temperature. The lat- ter would say there is no such definition of “the response of fration is (nearly) mineralized and respiration rates are nearly soil respiration to temperature” as a whole, but defines how constant, (3) to fit a model of C mineralization combined with individual components—e.g., rate constants of decomposi- a temperature-response function of the rate constants to the tion, root maintenance, and growth respiration—depend on mineralization curves. With approaches 1 and 2, only a small temperature. These two very different approaches can lead part of a long-term incubation is considered. Moreover, at the to very different results that are per se not comparable as will beginning of an incubation, soil respiration may still be influ- be outlined in the next sections. enced by disturbance, introduced by sample preparation (Blet-Charaudeau et al., 1990; Schinner et al., 1993), while at the end of an incubation, inhibiting metabolites may have 4.1 Analyzing soil respiration at the laboratory accumulated, which could adulterate the temperature de- scale pendence of C mineralization (Kirschbaum, 1995). Therefore, it is strongly recommended to fit a model of C mineralization Measuring and modeling soil respiration in the laboratory has combined with a temperature-response function of rate con- got the advantage that the influence of different factors can stants to the temperature-dependent mineralization curves be analyzed under controlled conditions. Disadvantages of (e.g., Kätterer et al., 1998; e.g., Updegraff et al., 1995). This such method can be summarized under the notion of introdu- approach provides the temperature dependence of decompo- cing artificial conditions that are not further discussed here. In sition rate constants, and, additionally, the model is compati- the laboratory, usually only respiration stemming from the ble with current C balance models (e.g., Andrén and Kätterer, mineralization of SOM is observed, while roots are either 1997; e.g., Parton et al., 1987), which also use temperature- sieved out or considered inactive, since they do not get any dependent rate constants. supply of photosynthates. Thus, with such experiments it should be possible to easily obtain the temperature depend- ence of SOM mineralization. However, even in this case the situation is not as “controlled” as it might appear, mainly due 4.2 Analyzing soil respiration at the plot scale to the dynamic nature of the decomposition process (Fig. 3). At higher temperatures, the easily decomposable fraction will The rapid development of soil respiration chambers with reli- be mineralized more quickly than at lower temperatures. That able infrared gas-analyzers has made possible diurnal as implies that after a certain time, there will remain more easily well as year-round observations of in situ soil respiration. decomposable matter in the low-temperature treatment than These studies have also been used to derive the response of in the high-temperature one. The result is a relatively higher soil respiration to environmental factors, most often being soil soil-respiration rate in the low-temperature treatment after a temperature and water availability. However, the observed re- certain time, i.e., a decreasing Q10 with incubation time. sponse can be easily confounded by other biotic or abiotic When the easily decomposable fraction also in the low-tem- factors, so that care has to be taken when interpreting and perature treatment is nearly completely decayed, then the extrapolating the results, e.g., in the context of global change. Q10 rises again. So, the Q10 dynamics is a result of the chan- Here, the effect of seasonally varying factors and the effect of ging amount of decomposable matter in the different temper- fluxes coming from different soil layers are discussed.

AB Figure 3: (A) Theoretical dynamics of the available SOM 10 substrate during an incubation experiment at high (lower curve, dashed) and lower temperature (upper curve). (B) Resulting apparent Q10 time series that would result from relating the instantaneous fluxes from the high- and the Apparent Q low-temperature treatment (see Reichstein et al., 2000, Available substrate for details and real-data analysis). The Q10 relationship was only used for simplicity; the principle holds true for Incubation time any function.

 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim www.plant-soil.com J. Plant Nutr. Soil Sci. 2008, 171, 344–354 Soil respiration across scales 349

When analyzing seasonal variation of soil respiration, the pro- those examples that these empirical apparent Q10 values are blem is that several factors co-vary (e.g., temperature, moisture, not compatible to what is used in mechanistic models. plant assimilation, root activity). When the variation is then attributed to one factor only, background correlations with other factors can confound the relationship. A typical situation is 4.3 Analyzing soil respiration at larger scales depicted with the temperature–soil respiration relationship in Fig. 4. In a summer-active ecosystem (e.g., a summer-green Analyzing soil respiration at larger scales brings the spatial deciduous ), the general higher biological activity in sum- dimension into play, where site-to-site variability needs to be mer adds on to the “pure” or direct temperature response. In modeled. From site to site all factors that were discussed such an ecosystem, the true temperature sensitivity would be above potentially (co-)vary by large magnitude. Thus, a direct overestimated using seasonal data. The opposite effect occurs link from empirical results obtained at this scale to mechanis- in summer-passive (e.g., summer-drought-affected ecosys- tic model parameters is even less possible than from results tems, cf., Fig. 4). One prominent example of such a misinterpre- at the field scale because of the confounding effects. For tation of seasonal data is the study from a trenching experiment example, a result showing that decomposition rates did not (Boone et al., 1998), where an (apparent) stronger temperature vary significantly with temperature along a continental gra- sensitivity of root respiration compared to the bulk soil respira- dient (Giardina and Ryan, 2000) does not invalidate the fun- tion was found. In view of the fact that the actual temperature re- damental temperature dependence of decomposition rate sponse of root respiration does not differ from soil respiration constants that is used in C-balance models. Instead the cor- (Bååth and Wallander, 2003), this result can only be explained rect interpretation is that there are other factors that override by a stronger seasonality of root respiration, hence a spurious the temperature effect. result. Also it cannot be ruled out that strong decline of Q10 at higher temperatures in the review by Lloyd and Taylor (1994) is partly caused by interaction with soil moisture limitations, i.e., Similarly, there has been some controversy about biological that the currently most commonly used function is a spurious or and climatic controls of soil respiration stemming from differ- confounded one. ent interpretation of large scale analysis. In several studies, Raich and coworkers have shown that large part of spatio- The relation between observed in situ respiration rates and temporal variability of soil respiration can be statistically soil temperature is also ill-defined since soil respiration is ori- explained by monthly temperatures and precipitation, i.e.,by ginating from different depth with each depth having its own purely climatic drivers (Raich and Potter, 1995; Raich et al., temperature dynamics. Depending on which depth for soil 2002). This apparently contrasts other findings that productiv- temperature is used as a predictor in the regression with soil ity (biological control) is the main determinant of soil respira- respiration, varying temperature sensitivities will result: the tion across continental scales (Janssens et al., 2001; Valen- deeper the soil-temperature measurement, the smaller is the tini et al., 2000). But again, these are only correlative relation- amplitude of temperature and consequently the larger will be ships being obscured by the background correlation between the estimated temperature sensitivity, e.g., the Q10 (cf., productivity and climate. With a careful analysis, it may be Fig. 5). Theoretically to solve this problem, one would have to possible, however, to statistically separate biological and cli- fit a multisource model to the respiration data, but experience matic controls on soil respiration. Reichstein et al. (2003a) shows that such a model is often overparameterized. One have done such analysis and showed that both categories work-around is to use the temperature at that depth where are important for describing spatial and temporal variation of the best correlation is obtained (in the example 5 cm). Never- soil respiration, with a model that used temperature, precipi- theless, temperature sensitivities obtained from different tation, and leaf-area index as predictors. While this model is studies are only partly comparable, even if the depth is stan- also statistical, it better accounts for variations caused by bio- dardized, since thermal properties (insulation) differ between tic and abiotic factors, e.g., with respect to interannual varia- soils (and even seasonally within the same soil), as well as tions of soil respiration, that were very small according to the the depth of main respiratory fluxes. It should be clear after climate-driven model.

Confounded response summer active

‚ Direct‘ truerue response to temperature

Confounded response summer passive

Respiration Figure 4: Schematic representation of the confounding effects introduced into a temperature dependence of soil respiration derived from annual data. Triangles and squares are hypothetical data for summer-active and Temperature summer-passive ecosystems, respectively.

 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim www.plant-soil.com 350 Reichstein, Beer J. Plant Nutr. Soil Sci. 2008, 171, 344–354

30

25

20

15

10 Temperature [°C] Surface 5 5 cm 10cm 0 10.07. 12.07. 14.07. 16.07. 18.07. 20.07. 22.07.

6

5 ] -1 s 4 -2

3

2 Rsoil m [µmol 1

0 10.07. 12.07. 14.07. 16.07. 18.07. 20.07. 22.07. Date

7 7 7 y = 1.0065e0.0688x 6 6 R2 = 0.9359 6

] 5 ] 5 ] 5 -1 -1 -1 s s s -2 4 -2 4 -2 4

3 3 3

2 2 2 Rsoil [µmol m [µmol Rsoil m [µmol Rsoil m [µmol Rsoil 0.0775x y = 1.4642e0.0461x y = 0.8847e 2 1 R2 = 0.6815 1 1 R = 0.5299

0 0 0 010203001020300102030 Temperature [°C] Temperature [°C] Temperature [°C]

Figure 5: Upper panel: Soil temperature at soil surface, 5 cm, and 10 cm depth; center: soil respiration; lower panel: scatter plots of soil respiration vs. surface, 5 cm, and 10 cm temperature (from left to right), with fitted exponential function. Artificial data.

4.4 General strategies for linking observations other ecosystem flux data (Fig. 6): In the forward approach, and models across levels different C-balance models are tested if they are able to gen- erate the spatial or temporal patterns (e.g., continental or We have discussed several instances where a direct transfer environmental gradients) that are empirically observed. An of empirical relationships, e.g., from the ecosystem level to important task in this approach is actually to define and iden- the process level is misleading, as in a generalized way tify the important general patterns in the data that needs to depicted also in Fig. 6. Instead of trying to directly establish be reconstructed by a “good” model. In the inverse approach, fundamental relationships (like temperature dependence of model parameters at the process level are inferred from eco- decomposition rate constants) from large-scale pattern there system-level observations, such that the model reaches a are more fruitful approaches to analyze soil respiration and maximal consistency with the observation. Inferred para-

 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim www.plant-soil.com J. Plant Nutr. Soil Sci. 2008, 171, 344–354 Soil respiration across scales 351 meters can then be confronted with theoretical expectations Table 3 summarizes ecosystem processes across scales at the process level. Bayesian model-data synthesis to some which importantly contribute to the overall soil respiration. For extent mediates between these two approaches, in the sense being able to explain as much observed phenomena across that a model is constructed that obeys both the data and prior scales as possible, we propose to build and constrain a land- expectations about parameter at the process level (Knorr and scape-scale model of soil C dynamics by using as much infor- Kattge, 2005; Reichstein et al., 2003b; Tarantola, 1994). mation as possible from observations at different scales Regardless of the method applied, often the problem is (Fig. 7). Observations in aggregates in conjunction with underdetermined, i.e., the data is not sufficient to distinguish studies will increase our understanding about between model structures or parameterization. In these temperature and moisture dependencies of dynamics of cases, it is crucial to define new observations that exert microbes, biochemical kinetics of C decomposition, and auto- further constraints on the models (multipleconstraint trophic root respiration. This leads to a first dynamic process approach). With respect to soil respiration, this implies that model operating on spatial and temporal fine scales. more attention should be drawn to collect not the flux data themselves but also information about system properties, like soil C fractions, soil microbial biomass, and their vertical dis- At the pedon scale, many of the required variables are not tribution. observable anymore. Instead, a scaling model has to predict the quantities emerging of reaction surface area, moisture, and temperature at which the underlying biochemical reac- tions take place. Since representation of environmental con- ‘Real’ world Model world ditions, which occur at the aggregate level, is not known a Inverse priori at the pedon scale, parameters have to be re-estimated approach Ecosystem level Ecosystem level at this scale. Parameters for both scaling and condition repre- sentation can be obtained by inverse modeling (see above) of the enhanced process model against measurements of soil respiration and C profiles. At the same time, the temporal coverage of this scale might be higher, thus temporal variabil- ity from day-to-day to interannual are represented by such ‘Process’ level ‘Process’ level reparameterization. In addition to scaling the reaction area Forward and representation of environmental conditions, there are approach processes at the pedon scale which are not observable at Figure 6: Scheme of inappropriate (crossed out) and alternative fine scale, e.g., cracking higher organic structures or spatial ways of linking model and observations across scales. Direct replacement of organic material (OM) by macrofauna (rain comparisons should only be performed at corresponding levels. In worms etc.). These processes might be represented sepa- the forward approach, process-level observations (“system com- rately in the pedon-scale model, and kinetic-related para- ponents”, e.g., root biomass, soil organic-matter pools, temperature meters have to be retrieved in a classical way. On the other sensitivities of those) are put together in a model that predicts hand, such processes could act as intermediate steps in the the behavior at the whole (eco-)system level. These predictions can decomposition of products (OM) to educts (CO and H O). then be compared to direct observations at the ecosystem level. In 2 2 the inverse approach, model parameters at the process level are This would either change the whole kinetics approach or just inferred from ecosystem-level observations, such that the model modifies the parameters derived at aggregate level. In the lat- reaches a maximal consistency with the observation. Inferred ter case, the Bayesian inference is preferred again for para- parameters can then be confronted with theoretical expectations at meter retrieval. Effects of aboveground productivity on soil the process level. respiration mediated through root exudation could be also

Table 3: Processes, heterogeneity, and observables of soil respiration at different scales. Processes occurring at lower scales are also repre- sented by observations at larger scales, also when not repeated in related table rows.

Spatial scale Temporal scale—affected Process Represented heterogeneity Observable organics compounds

Laboratory and partly sub- seconds to days—high labile respiration of roots, bacteria, no Soil CO2 efflux, pedon (process level) organic matter and fungi; population [C] change dynamics of microbes Pedon (ecosystem level) days to years—medium root exudation, i.e., vertical distribution of organic soil respiration, labile compounds productivity effects, matter and abiotic factors mean [C] aboveground autotrophic change, respiration, catalytic effects C profile of meso- and macrofauna and their respiration Plot and landscape years to millennia–-ore turnover of less labile horizontal distribution of spatial details (ecosystem level) stable compounds organic matter organic matter, macrofauna, of C storage, and environmental abiotic forms conditions

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Figure 7: Scheme of a model which is thought of being able to interpret observations across various scales. The first dynamic process model built upon fine-scale observations is extended and reparameterized by observations at pedon and landscape scale via the Bayesian inversion technique. Model enhancement includes scaling of reactive area from one scale to another as well as the representation of new processes. Representation of fine-scale observations at higher scales is not known a priori. The application of the final model at landscape scale results in dynamic ecosystem properties and continental-scale C storage that can be compared to independent estimates. clarified at this scale if whole-ecosystem (e.g., eddy covar- References iance) flux measurements were available. Amthor, J. S. (2000): The McCree–de Wit–Penning de Vries–Thornley Respiration Paradigms: 30 Years Later. Ann. Bot. Finally, pedon-scale conditions have not necessarily to be 86, 1–20. representative at landscape scale (between-site variability). In addition, environmental conditions like soil moisture and Anderson, J. M. (1991): The Effects of Climate Change on Decompo- sition Processes in Grassland and Coniferous . Ecol. Appl. temperature vary even more than at the pedon scale and 1, 326–347. also with time because of variable soil properties and micro- relief. Thus, parameters for the prediction of the product of Andrén, O., Kätterer, T. (1997): ICBM: the introductory carbon balance model for exploration of balances. Ecol. Appl. surface area, moisture, and temperature, as well as process 7, 1226–1236. parameters should be re-estimated by using observations like spatial details of total C storage or humus forms, also via Andrén, O., Paustian, K. (1987): Barley Straw Decomposition in the Field: A Comparison of Models. Ecology 68, 1190–1200. a Bayesian approach. The application of such ecosystem model representing dynamic vegetation and soil fauna at a Arrhenius, S. (1889): Über die Reaktionsgeschwindigkeit bei der landscape scale leads to spatial details of soil C content and Inversion von Rohrzucker durch Säuren. Z. Phys. Chem. 4, dynamic ecosystem properties, that are to be evaluated by 226–234. independent estimates from data-oriented upscaling. In doing Bååth, E., Wallander, H. (2003): Soil and rhizosphere microor- so, different locations for model development and validation ganisms have the same Q10 for respiration in a model system. have to be chosen. Glob. Change Biol. 9, 1788–1791. Birch, H. F. (1958): The effect of soil drying on humus decomposition and availability. Plant Soil 10, 9–31. 5 Conclusion Blet-Charaudeau, C., Muller, J., Laudelout, H. (1990): Kinetics of Carbon Dioxide Evolution in Relation to Microbial Biomass and Soil respiration at ecosystem scale is the result of various Temperature. Soil Sci. Soc. Am. J. 54, 1324–1328. processes occurring across orders of magnitudes in the spa- tiotemporal domain. Since most of the responsible species Boone, R. D., Nadelhoffer, K., Canary, J. D., Kaye, J. P. (1998): Roots exert a strong influence on the temperature sensitivity of soil are not known, a holistic representation of metabolic activity respiration. Nature 396, 570–572. of roots and microorganisms seems to be appropriate at the finest scale of clay aggregates. Careful experiments at this Borken, W., Xu, Y.-J., Brumme, R., Lamersdorf, N. (1999): A Climate Change Scenario for Carbon Dioxide and Dissolved Organic scale are pivotal to the parameterization of a dynamic pro- Carbon Fluxes from a Temperate Forest Soil: Drought and cess model of autotrophic and heterotrophic respiration. Rewetting Effects. Soil Sci. Soc. Am. J. 63, 1848–1855. Observations at pedon scale (chamber measurements, C Borken, W., Davidson, E. A., Savage, K., Gaudinski, J., Trumbore, S. profile) and at landscape scale (C-storage maps) are impor- E. (2003): Drying and Wetting Effects on Carbon Dioxide Release tant to include processes at larger scales and to account for from Organic Horizons. Soil Sci. Soc. Am. J. 67, 1888–1896. scaling effects. In doing so, the information gained at lower Bunnell, F. L., Tait, D. E. N., Flanagan, P. W., Van Cleve, K. (1977): scales is utilized at higher ones by applying the Bayesian Microbial respiration and substrate weight loss. I. A general model approach. of the influences of abiotic variables. Soil Biol. Biochem. 9, 33–40. Carlyle, J. C., Than, U. B. (1988): Abiotic controls of soil respiration beneath an eighteen-year-old Pinus radiata stand in south-eastern Australia. J. Ecol. 76, 654–662.

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